That monitor is capable of 30-50kHz horizontal, 47-90Hz vertical. Yes, it will be limited in what vertical refresh rates you can choose at 1024x768. The number of lines and the vertical refresh rate determine the horizontal scanrate: vrefresh * totallines = hscanrate (totallines is slightly higher than the number of visible lines, so it's a bit more than 768, here - VESA GTF gives you 806 total lines). Hence, you can only go up to 50kHz/806 = 62Hz refresh at 1024x768. You could go all the way down to 47Hz (47Hz*806=37.9kHz), if you like, but it will have very noticeable flicker.
You can run 640x480 at up to 90Hz (525 * 90Hz = 47.25kHz), if you want. The minimum would be ~60Hz as that bumps up against the 30kHz lower limit. 800x600 would have a minimum refresh of ~48Hz and maxmimum refresh of ~79.5Hz.
You cannot run native 15kHz timings on that monitor as 15kHz is less than 30kHz. This means you can't do 480i or 240p type modes. The minimum for that monitor is basically 640x480 @ 60Hz, and the maximum is 1024x768 @ 60Hz, all progressive. You COULD run native 15kHz timings on the other Makvision monitor that Happ is selling (the analog CGA/EGA/VGA one), but then you give up the ability to do 800x600 or 1024x768 progressive (you can still do it, but you have to interlace it which introduces jitteryness and flicker).
In general, exact 2:1 stretches don't do much to the overall look of the video aside from removing some scanline effects. In fact, the monitor can't tell where the pixel boundaries are on the horizontal axis at all! You can do a 2:1 scale horizontally (leaving it the same vertically, so a 640x480 image would become 1280x480), and you shouldn't be able to tell the difference as the active video signals are identical (in most cases - some video cards will output something subtly different).
What's this mean? This means that, if you want to run old arcade games, which were usually ~240p, on a high res monitor, you should run it at exactly double the resolution with the same refresh as originally. This will eliminate tearing artifacts and should minimize any evidence of scaling (again, you'll just change the scanlines). So, if the original game ran at 342x244 (to pick somewhat random numbers), running at 684x288 should give you something that's as close to the original video as your monitor is capable of displaying. YMMV, and I have no idea how to tell MAME to do that, but I'm guessing it can.
FYI, CRTs don't really have a "native resolution". Unlike LCDs and plasmas, which have discrete pixels directly mapped to input video pixels, CRTs just have an array of phosphors that you can draw anywhere on. Some low end CRT HDTVs (which are rare beasts, these days) are only capable of a single resolution and scale everything to that, but these multisync arcade monitors will directly display anything you feed them without any scaling. They don't even have the hardware necessary to perform scaling.