Yes and no.
64-bit OS (in this case Windows 7) does not make 32-bit program run faster, however 32-bit OS can not run 64-bit programs.
64-bit program is also not always faster than 32-bit counter-part assuming there is one.
As a matter of fact, if 32-bit and 64-bit programs are doing the exactly same thing, 32-bit program will run faster.
Having said that, 64-bit programs are generally newer, does more and designed to take advantage of 64-bit architecture has to offer thus run faster than its previous generation 32-bit programs.
It is more apparent in CPU/memory intensive applications like (Photoshop, Encoding, and so on).
If programs you have are all 32-bit programs, there should not be any compelling reason to upgrade to 64-bit.
On the other hand, if you want to take advantage of 64-bit architecture (such as more than 4GB memory) and applications in 64-bit edition,
you can consider installing 64-bit OS (Windows 7) because 64-bit OS will run 32-bit programs.