Yes—an APS-C sensor uses a smaller central portion of the lens’s image circle, so edge darkening from stacked filters is generally less likely to show up than it would on full frame.

There isn’t a simple universal multiplier, because filter-induced mechanical vignetting depends on lens design and especially focal length. Wide-angle lenses are usually more sensitive than longer lenses.

In practical terms, with most full-frame lenses on APS-C, you would need quite a lot of extra filter thickness before the crop sensor sees the vignette. One answer estimates the corner difference between full frame and APS-C is roughly 8mm diagonally, so if each added filter effectively narrows coverage by about 1mm all around, it could take around 8 stacked filters before it becomes visible on APS-C.

So the basic idea is correct: crop sensors tolerate stacked filters better. But the exact amount is lens-dependent, and for most normal uses the number of filters required would be excessive enough that stacking itself would be a bigger concern than the vignetting.