The Atmega16 and Atmega32 are pin compatible, the code will likely have to be re-compiled possible some of it ported though as registers have changed. It may not work with the software that was designed for the dev board but it will not harm anything to try it.
Not at all Ian. Here's a link to the board he's talking about.
I'm not sure why he said they're not cheap though, that board shouldn't have cost more than 10 dollars. It should work fine with a Mega32, with the exception that none of the code will work until it's recompiled with the new I/O space that's in the Mega32. The programmer's software itself (no idea what it uses) may have a problem with the Mega32 but it won't hurt anything.
Simply put, it will work or not, it can't damage anything.