I've never seen or heard of an arcade monitor supporting DDC EDID (the means by which monitors communicate their capabilities to the video source), so chances are it does no, however, Billabs does have monitors which go up to 1024x768@60Hz, and include 800x600@60Hz capability, which is the default resolution of WinXP and some Linux distributions when they don't know what monitor is hooked up. From there, you can reconfigure at will.
Also, I don't know why you'd need an ArcadeVGA at all for a trisync unless your video you had before was incapable of doing EGA/CGA modes (there was a time in there for about 4-5 years were most stuff nVidia and ATi shipped couldn't, but most stuff seems able to again). Just boot with a PC monitor hooked up, reconfigure for 640x480 (VGA), and then hook up the arcade monitor. You should only have to do this once. In WinXP, the 640x480 option is hidden (go into Advanced, Monitor, List All Modes), but it's there.