That's where the "sense pin" thing comes in. I've not tried it, but I'm fairly certain the answer is "no". The limits of that connector, in my limited experimentation with one of those Mac monitor adapters that let you "dial a res", IE, make a VGA multisync monitor emulate any particular Apple Monitors, seem to boil down to either detecting the iMac's build in monitor (which supports three oddball resolution/sync combinations) or the "Multisync" setting supported by later Quadras and PPC Macs. the 12" RGB doesn't even support fixed-frequency VGA scanning rates.
Yes, it doesn't support dual monitors or anything.
Your built-in monitor's flyback transformer *will* fail eventually. It's inevitable. It's likely the only reason it works at all now is the machine sat in a closet for so long. I was given two Bondi iMacs all the way back in 2000 and one already had a failed flyback and the other was in the process of failing when I gave it away a few years later. (And I'd probably used a total of, I dunno, maybe a hundred hours during those years.) This is why ATX case/power supply conversions were so popular for these machines years ago. I did a power supply conversion myself... I never got as far as actually recasing the iMac motherboard because it dawned on me that an iMac wasn't any more useful in a new case than it was in the original.
If you've never had a Bondi before, reacquaint yourself with their Byzantine quirks when it comes to hard drives. Short version: They're picky about which ones they like, and that "First 8GB" OS partition limit for OS X? Apply it to OS 9 installs too, or you might end up regretting it.