As dv8 said, yes, it will install and run on a 32 bit OS.
However, while I don't know your situation at work, let me add that if you are working on images of modest size or larger (say 3000 pixels on the shorter dimension, and a bunch of layers), you really need to change your work computer to a more modern one with a 64 bit OS. The increase in speed and stability / reliability will be well worth it. In addition, if I am not mistaken, I think that Adobe has stopped supplying 32 bit versions of the most recent releases of PS, so you are shut out from all the new tools and other improvements they have made.
Just my $0.02,
Tom M