If you are concerned about the impact of whatever difference in calorie count cooked vs. raw makes, you are cutting it pretty fine. The margin for error is likely very small--probably smaller than your measuring errors, or the inaccuracy of your kitchen (or bathroom) scale.
Keeping an eye on calories is fine for weight loss. Reducing calorie intake and/or increasing calorie burning is the only proven way to do it. But looking out to avoid that 20 calorie margin of error suggests that either you're not cutting enough calories in the first place that 20 matters, or you're tormenting yourself over things you shouldn't be worried about. Cut yourself some slack, and don't sweat the small stuff. The simple act of realistically monitoring how much you eat is more likely to help you than obsessing over every single calorie.
If you are interested in the theory, the answer is yes, there is a change. If you are interested in dieting, the answer is still yes, but it is quite irrelevant to you.
There are two types of browning reactions, Maillard and caramelization. Both start with highly complicated molecules and end with different kinds of highly complicated molecules. For a very precise answer to your question, one would have to know every possible chemical reaction occuring there, the energy trapped in the precursors and in the resulting molecules, and whether this energy is accessible for the human body (e.g. there is quite a lot of energy in raw petrol, but your body can't extract it if you happen to eat it). As these reactions haven't been studied in this level of detail, it isn't possible to give you a really precise answer.
On the other hand, the tendency would be for the calories (at least the digestible ones) to fall somewhat. First, the calories from amino acids and carbohydrates (which are the inputs for browning) are digestible; some of the reaction products can be digestible, but not all will be. Second, some of the calories will literally disappear in thin air - because some of the products of these reactions are volatile.
But if you are expecting to reduce your dietary calorie intake by eating toasted bread, it will probably make no difference at all. First, the calorie-reducing effects will only occur for a small part of the molecules involved. Second, and more important: even if it did occur for all molecules involved, browning only happens on the surface (theoretically, it could happen on the inside too, if you heated it in the 154°C - 190°C range. Practically, if you are doing that, nobody will want to eat that food). The surface is quite small as opposed to the rest - let's assume a slice with 1 cm thickness and a generous browning of 0.5 milimeter depth. (I know that the part which gets hard is thicker, but it doesn't really get browner). I'll disregard the surface enlargment caused by leavened-bubbles in the crumb (because I'm afraid I might end up with an infinite fractal surface :) ) and then we have ~10% of the slice browned. As I said, there is no chance that all the calories in this part disappear completely, and I doubt that the reduction will be really significant. But even if it was at really high 50%, you only get 5% reduction in total, or 10 calories per slice of white bread, less for diet-friendly breads (and this number is just an inflated best-case guess).
Best Answer
The best way to be confident is to check some clear nutrition facts directly.
The USDA reports that "Pasta, dry, unenriched" has 371 calories per 100g, and "Pasta, cooked, unenriched, without added salt" has 158 calories per 100g.
So your 176 calories per 100g seems to be for cooked pasta; it's way too few calories for 100g dry, even if your pasta is slightly different from the USDA's default.
Calories per gram when cooked is going to vary a bit, because if you cook it a bit more or less, it'll take on a bit more or less water. So the same amount of dry pasta, with the same amount of calories, may weigh slightly different amounts.
Also, I looked at the page you linked. Down at the bottom it says:
And indeed, along with per 100g nutrition facts, it has a per 170g column. So yes, it appears that those nutrition facts are for cooked pasta.