Wouldn't this be be exactly double of NTSC, in which case the TV would
see every other frame of the composited VGA?

If the TV would ignore the sync pulses that arrived too soon, you might get
two images, side by side. But that ignores the other complications that I
didn't mention: VGA and NTSC don't use the same vertical sweep frequency.
And NTSC is an interlaced vertical scan, meaning you get alternating lines
of display, rather than a complete image scanned top down. NTSC requires
two complete top down scans to get all lines of an image. VGA is
non-interlaced.

Or, because I am intending to run the card in Linux, could I create a
resolution below
640X480? But you may be right, a surplus video card with S-video out
would sidestep this problem.

The video card has more to do with the VGA scan rates than the operating
system. You often see crystal controlled oscillators on video cards so you
are locked into what the card manufacturer provides. I can't rule out
some flexibility here, but I think a video card with NTSC video output would
be the surest way to get this idea to work.

Roger