Will a 32 bit intel app run on Mountain Lion?
For a generic 32bit Application the answer is yes, confirmed yourself with Google Chrome. it should run just fine.

Now for Utility programs, and programs that interact directly with OS X specific features, the answer will likely be no, those programs will need updates to run at their best. 

Applications interacting with hardware, will also likely need updates or tweeks to their drivers in order to work.

Other than that you should not have to worry about running 32bit programs on Mountain Lion. I would try checking the developer's websites for Mountain lion compatibility to be sure on your expensive mission critical apps before upgrading full time to Mountain Lion.