I have a 722 in 257 improved and was thinking of putting it in a 700 sa adl stock. I am just wondering if there is any problem with putting it in an ADL stock. Or will it only go in a BDL stock?

I put a 722 300 savage in a bdl stock. Shoots great. It was very easy to do, did not try an adl stock.

It is not difficult but several things must be done.
1) the safety lever either needs to be replaced to a 700 safety lever which requires a small notch be filed in the action rear tang. Or you can keep the 722 safety lever and make room for it alongside the tang (remove some of the stock).
2) You will need an ADL triggerguard.
3) Your magazine box is going to be too deep so you may need to cut it down or replace with a 700 box.
4) Watch the length of the action screws, especially the front as it will bind the bolt if it is too long (almost always).

Oh, forgot to add, on 1) I much prefer to notch the action tang.

Here's a 722 in an ADL stock, in fact I have two ADL stocks for it and will be doing a third. If it is the original barrel you will have to inlet the forend for the dogknot rear sight base. I did this on an ADL walnut stock for the original 300 Sav. barrel.

I don't think I had to shorten the mag for either stock. I used the original trigger and safety and inletted the stock for it. I did have to open the slot in the bottom of the stock as it rubbed on one side. Clearance needs to be made for the original bolt handle.

This one has a 300 Sav. barrel and a walnut 700 ADL stock, a 22-250 LVSF barrel and ADL synthetic stock(shown) and will get a 22-250 heavy varmint barrel and synthetic ADL stock this summer.

Not all 722s came with the dognut and not all 700s came without...