No, shouldn't make a difference.
Am I going to need much more processing power to convert the digital HD stream to an analog VGA signal to output to my TV?
No, not from mythtv's side.
Will this add more delay when I am watching live TV (and thus more delay in changing channels)?
Maybe, maybe not - this more depends on how well your TV set processes the different signals. It a similar argument people have with component in vs. DVI-D/HDMI. In some cases, component can look better even though it is analog. For most people on most sets, the difference in negligible IMHO.I assume that I have to at least lose some quality (but from the sounds of it, probably not a real noticeable amount).