will my adobe photoshop CS2 work if i upgrade to snow leopard

It should, as long as you remember to install Rosetta (a PowerPC emulator). If you check Adobe's site, it says:

Mac OS X v.10.2.8 through v.10.3.8 (10.3.4 through 10.3.8 recommended)

But that doesn't mean it won't run in Snow Leopard. Adobe always lists their system requirements by what they officially support for each version.

Roaring apps is usually pretty good for finding such information, but they no longer even list compatibility for any version of the Mac OS older than Mavericks, 10.9.x. The site also needs a serious cleaning up. Such as this. A search for "Photoshop CS" turns up everything they list for various versions. They list the original CS, which will most definitely not run under Mavericks, then skip listing CS2 and CS3 altogether. Then they have CS5 listed three times. One of which marks Mavericks with a red X. Also wrong.

Not True.

Roaring Apps still lists all older OS X versions, you just need to modify the chart by selecting the Options buttons.

Snow Leopard, Lion and Mountain Lion can get added to the default chart view.

Check here.

http://roaringapps.com/

Ah! There they are. Didn't notice you could adjust what was listed.