Could you do it... Yes. There are a few problems with this setup.
First, if the saw does not have a locking trigger how will you turn it on when you are cutting? If it does have a locking trigger, you'll want a way to turn the tool on/off quickly and easily. This could be achieved by connecting the saw to a power strip, and mounting the strip in an easily accessible area. You'd then use the switch on the power strip to turn the saw on/off.
Will mounting the saw make changing the blade difficult/impossible?
Mounting a jigsaw in this way could make it easier to force the wood, which could lead to binding, flexing, and even cause the blade to break (which could be deadly).
Lastly, why are you using a jigsaw for long straight cuts? Long straight cuts are far easier with a table/circular saw. The great thing about a jigsaw, is that the blade can bend and flex slightly. This makes cutting contours easier, but will make long straight cuts more difficult.
A reciprocating saw WILL do the job. If that is what you have and you do not wish to buy/borrow/rent a chainsaw, then you can use it. Get a long blade, designed for cutting wood. These blades have large, sharp teeth with wide gullets between them.
The reciprocating saw will take longer to do the job, and it does have some vibration issues, but I can assert that you can use it for hours at a time. A good saw is a beast, designed for heavy duty work. (I did so to cut up the wood after we had an ice storm once. It left piles of wood behind that can only be measured as many cubic yards. My chainsaw was dead, and was painfully unwilling to be revived. Amazingly, I used only 3 blades for the entire job. The final pile of wood and brush was roughly 10 feet wide, 6 feet high, and 60 feet long.)
If you do use a reciprocating saw for this purpose, you might buy some gloves with padding in the palms. Good gloves will be a necessity anyway, so use them. Ear protection is a good idea too.
If you already have a reciprocating saw and a circular saw, and want to just buy the right blades ... I'd consider a carbide blade in the circular saw, using it for wood that is up to 3 inches thick. Choose a blade with few teeth and large gullets. Then use the reciprocating saw with a wood blade only for those pieces that are too thick.
Having said all that, perhaps another solution if you do not wish to buy a gas powered chainsaw, is an electric chainsaw. These saws have no issues with gasoline, so are slightly simpler to deal with. It is still a chainsaw though. You will still need to use oil, and kickbacks are still a problem to watch out for, but a circular saw can also be dangerous if used unwisely.
Replace or sharpen dull blades as appropriate. A dull blade is a dangerous blade. It takes more effort to use, so you push harder. A good saw with a sharp blade should almost glide through the wood.
Finally, if you are cutting up a large amount of wood, then be careful. Do not work when you are tired. This is true using ANY saw. Stop and finish the job another day, a far better idea than spending time in the emergency room.
Best Answer
Score with a utility knife, clamp between scraps of wood, and snap.
If you don't have enough extra length to snap with, the best tool I've found is a grinder with a diamond blade. (Use outdoors with appropriate PPE.)
If you have to use a jigsaw blade, then yes, the grit ones will certainly outlast a wood blade, but not by much. (And maybe not enough to justify the added cost.)