To expand michaels answer (assuming that you want strawberry icecream and not pieces of strawberry mixed in).
If you are making a custard ice cream, leave the amount of egg yolks the same, because you want the lecithin from them. Reduce the sugar somewhat, because fruit is sweet. Then decide how much fruit puree you want (maybe 1/3 the volume of the dairy part). Adjust the volume of the dairy so that the liquid is correct. Adjust the fat of the dairy so that the fat content is correct.
Example, you start with the recipe for vanilla ice cream French (=custard) style by Lebovitz.
1 cup (250ml) whole milk;
A pinch of salt;
3/4 cup (150g) sugar;
1 vanilla bean, split lengthwise;
2 cups (500ml) heavy cream;
5 large egg yolks;
1 teaspoon pure vanilla extract
This recipe has 185g fat (I calculated with 30% fat in the cream), 460g dry matter (this is both fat and non-fat) and yields 990g ice cream (rounded a bit). Let's say that you decide to use 200g strawberry puree. 200g strawberry puree has 10g sugars, 18g dry matter and no fat. A mixture of 5 yolks, 140g sugar (if you want, you can look at the fructose sweetness coefficient and change the sugar accordingly, but I think this isn't so much of a problem if we just substitute the 10g from strawberries), 200g strawberry puree and some salt and vanilla has 25g fat, 225g dry matter and weighs 430g (rounded). You could create two equation systems, the first for the total volume of the dairy mixture needed, and the second one for the ratio of cream to milk, and solve these to get to a mixture with the original ratio.
fatamount/total = fatpercentage
liquidamount/total = liquidpercentage
fatpercentage + liquidpercentage + nonfatdrypercentage = 1
where you know fatamount, liquidamount and nonfatdrypercentage is around 0.1 (actually 0.08 for milk only and 0.12 for cream only, but we don't need so much precision). Solve for total, then calculate fatpercentage.
0.3*cream + 0.04*milk = fatpercentage*(milk + cream)
milk + cream = total
I will take a shortcut here. I specified almost as much strawberries as milk. They have no fat (unlike milk), but a similar (actually higher) amount of dry mass. So let's see what happens when we keep the 500g cream and turn the 50g difference between strawberries and milk into cream too (because we suspect we want some more fat). Then we have 190 g fat, 290g dry matter and 980g ice cream base. At 19.38% fat, we are above the ratio given in the article, but close to the original ratio (and I suspect that the article might be about Philadelphia style ice cream, which has less fat). The 29.59% dry matter are again outside of the article recommendation, but close to the original recipe. In fact, I assume that well emulsified fat can prevent ice crystal creation, so the higher liquid content doesn't create problems here (also note that McGee gives a 10-20% range for fat in ice cream, not 7-12%).
Long story short: don't add fruit puree, it is mostly water. Substitute puree for milk, calculate the new percentage of fat and dry matter (use the 7-12% fat and 37-42% liquid for a recipe without emulsifiers, you can be freer if you have emulsifiers; egg yolk counts as emulsifier). If you are still not there, try the calculation with less puree, or increase the fat and/or dry matter until you are in the recommended range. Or just start with the equations.
NB #1 I didn't check my calculations, could have a mistake there. But the principle should be correct.
NB#2 I calculated with cream density of 1. This was somewhat surprising, but the nutrition data for cream I found insists that a cup of cream (240 ml) weighs 238 g, so the difference is small enough to not go to the trouble to convert. A recipe given by volume probably (hopefully) has some leeway, so this shouldn't skew the results into a bad recipe.
Ice cream needs a certain ratio of solids to liquids to work. Sugar is an important solid in ice cream. As applesauce is mostly water, you can't replace all, or even most of the sugar.
The amount of carbohydrates in applesauce will vary depending on how much you cooked it down, but based on a few nutrition data results for the commercial variety, it seems that 40% carbohydrates is a reasonable assumption. So you want to remove some sugar and milk and add the applesauce and some butter (to compensate the missing fat). Calculating with 8% non-fat solids and 4% fat in the milk, and 83/17 fat/water ratio in the butter, we get following substitution: for each 10 g of sugar you remove, you also have to remove 20 g of milk, and add 29 g of applesauce and 1 g of butter. You probably need a recipe with emulsifiers to get the butter into it.
Most ice cream recipes will have much more cream than milk, and so not much milk available to remove. You'll have to recalculate to get the amount of butter needed when you are replacing cream. But the more dairy you remove, the more you are changing the flavor. While the texture is likely to keep up well (the pectin from the applesauce will probably do a good job to reduce ice crystals), the taste will move in direction sorbet. Depending on your expectations, this might be OK for you, or it might be a problem.
As for reducing sweetness, I am not sure this will happen. At very cold temperatures, sugar loses much of its perceived sweetness. Fructose loses some, but not all. And apples are very high in fructose. So, even though not all carbohydrates in applesauce are sugars, you might end up with a quite sweet ice cream. On the other hand, if you used sour-ish apples, the perceived sweetness will be low. There is no way to tell but try it out.
Best Answer
From a bulk perspective you don't have to replace sugar with anything, you certainly don't need want to add starch to compensate as that will not do favors for your consistency and mouth feel. Sugar helps the consistency of ice cream by reducing ice crystal formation, protein does not, and starch does a bit but makes your ice cream, well, starchy rather than creamy if you add much. Vanilla extract doesn't inhibit ice crystal formation much as it's not enough alcohol unless you add way too much, straight alcohol like vodka is a better choice.
For me the solution isn't bulk, but to make up for the lack of sugar using a stabilizer like guar gum and/or carageenan. Locust bean gum is good for presenting ice crystal formation as well.
Regarding sweetness, fruit isn't a good source of sweetness because of concentration. Most of fruit is water, and to add enough sweetness and fruit flavor you have to add a lot, adding a lot of starch, cellulose and water to your ice cream which isn't good for consistency. When I add fruit for flavor I cook it down into a jam to reduce its water content, this works well for berries, but wouldn't work for starchy fruits like bananas, you might try banana chips instead. I think what without some sort of sweetener it's going to end up pretty bland though.