I would not be surprised if it did, or did with some fiddling*, but I would not be surprised if it didn't. Definitely don't get one and expect it to work if you are depending upon it for something.
*assuming for a moment you have all 100 games (most are the same handful of games with some hacks for the other selections) then you potentially have quite a large save file and either have to write it to something else, make a big file or set a page. Today I could see having said games all in one save chip back to back, and having to slice out the game you want but I don't know what they will do in practice.
The ROMs themselves will likely not be dumpable without some effort with the source code and saves with repro type carts vary so much -- some are basically normal carts but some like the pokemon ones are anything but and nobody has looked hard enough at the GBA 100 in 1/lucky lucky man carts to know what goes.
Or if you prefer save up and get a proper flash cart.