I think it would be interesting to test on lower end DMMs, like average responding meters, or meters with just 50-400 Hz bandwidth. These are all pretty high end meters.
A few months ago, I tested this concept on Zoyi ZT219's and Aneng 870's? (both TRMS) as well as a couple of Harbor Freight throwaways (probably average responding) along with a half-dozen Fluke 87V's.
The TRMS meters all liked the DC square wave calibration checks and displayed expected results but the Harbor Freight clunkers' resolution was so bad you couldn't draw any real conclusions from them.
Interestingly, the Zoyi ZT219's proved to be more accurate when checking with the square wave than the Fluke 87V's (the 87V's read about 8LSD's higher at 100Hz) but the Flukes began to far outshine the others when the frequency was kicked up toward 1-2KHz.
NOTE: Both the 87V's and the Zoyi & Aneng's displayed similarly accurate TRMS results when tested on my sine wave modules.
SUMMARY: The square wave checkers work! Maybe not quite as good as a nice sine wave but sure as hell good enough, as mawyatt has indicated.
EDIT: Just dug up some old measurements I referred to above:
CD4047 Source Fluke 87V Fluke 87V Zoyi ZT219
100Hz SqWv 10.86VAC 10.87VAC 10.810VAC
21.63VDC
Unipolar