Although I'm not really an expert in electronics, I don't think it's really feasible. At least not employing the existing connection to the analog board, that is.
For that to work, the signal coming out of a compact Mac's logic board would have to be a CGA/EGA digital TTL signal, but as far as I know it's a really low level analog signal. I remember to have read somewhere that those logic boards actually drive the CRT directly, so I would guess that they must be generating something that ultimately drives the CRT gun without any fancy digital to analog conversion.
If someone could hack together a chip - say, an FPGA or something - that could sample the analog signal that's supposed to drive the CRT and process it on the fly into some more modern format, that would open up a lot of possibilities, but it's a pretty tough job. If I recall correctly there had been some attempts (possibly even here on these forums) to study the feasibility of such an adapter, but I think that nothing ever came out of them.
Another option would be to reverse engineer the Macintosh logic board and ROM/toolbox to find out exactly how the video memory is written, and try to hijack that information out of it. At this stage, the information to be displayed should reasonably be stored in some sort of "array" of pixels which could be "conveniently" read and converted by an external processing board to something actually drawable on a modern screen. Speaking as a programmer and software guy, this path would be a lot easier than the first one (not to say that's easy at all, but at least more feasible), especially since BMOW has already done extensive studies on the Macintosh toolbox ROM and the hardware architecture of the 512k/Plus - after all, his Plus Too project rendered everything via VGA!
That's just my two cents anyway, let's hear what the more experienced members say!