The short answer is - no...
Panther requires 128MB, although it can run on 64MB. Absolutely not with only 32MB, it won't even try. Your iMac is a Bondi-blue model, the first iMac. There's two RAM memory slots on the processor card. Some will be limited to a 256 + 128, or total of 384MB, others can take the maximum of 2x256 or total of 512MB - and you will struggle with finding memory that actually will work in those slots. You need PC-66 SO-DIMMs. PC-100, or PC-133 SO-DIMMs are _supposed_ to work, but you may find that you have to return several pieces that just refuse to be recognized. I think you will get the most success with a pair of 128MB chips.
Sounds like someone has replaced the original hard drive with something smaller! All those first iMacs came with a 4GB hard drive. Even that 4GB is not very much space for OS X in any version. 2GB hard drive would be a challenge! (or a big headache!) A custom install, to be sure, and removing all excess language support files will help.