I think it could be done, but it looks hard. Chapter 9 of Larry Pina's Macintosh Repair & Upgrade Secrets describes how to build an adapter to interface a compact Mac with a "PC-style TTL external monitor". It involves some soldering and building a simple circuit with some inverters. Then you could connect the output of the circuit to the TTL-to-VGA adapter you bought. But even then it might not work - as Gorgonops said, the horizontal refresh rate of the Mac video signal is not quite the same as typical PC TTL video. According to Pina's book, some TTL monitors worked better than others with a Mac video signal, and some didn't work at all.

Some months back, I proposed a different method of getting a compact Mac to VGA adapter and posted about it here. My idea was to use an FPGA or other similar hardware to grab the Mac's video data from the logic board connector, then buffer it, and "replay" it at a different horizontal refresh rate and with appropriate letter boxing etc. to make a standard VGA video signal. It should be possible in theory, maybe I'll try it someday.

Bbraun proposed a different technique using a fast microcontroller connected to the 68000 busses, and snoop for CPU writes to the frame buffer memory. The frame buffer is just a specific address range in normal RAM for the compact Mac. Then you'd have the Mac's screen image bitmap data, and could do anything you want with it: output it as VGA, save it to disk, send it over the network, etc. 

Let me know if you decide to try Pina's circuit - I'd love to see it tested in the real world.