Quite the contrary. The first thing "mende1" said was, "If you don't use your computer, the computer could go to sleep." when I explicitly stated that the computer was going to sleep WHILE tasks were running. The issue was never about whether or not the computer would go to sleep if I wasn't using the computer.
Additionally, I am quite aware that my iMac does not have Power Nap. That's why my post title was explicitly stating that I have an iMac with no SSD.
My question is why users without SSDs are forced to use power settings for computers with SSDs. Under previous OS X iterations, if there was processor or disk activity, the computer wouldn't go to sleep since stuff was going on. It wasn't required for the application itself to let the OS know it was doing something. Since there are more Macs without SSDs than there are Macs with SSDs, it seems odd that we aren't at least given the option to use the non-Power Nap power settings. Or that the OS knows that there is no SSD so it's going to use the previous power settings that worked for decades prior.
I was hoping there might be someone out there who knows the ins and outs of Mountain Lion/Power Nap/Apple better than I that could provide an explanation or solution. Setting my Mac to not go to sleep on an application per-use basis defeats the purpose of having energy saver settings at all.