Glyphosate interferes with aromatic amino acid synthesis, which is required by nearly all plants. I don't know what stopping the synthesis of the aromatic amino acids would do to the plant's vascular system, but it for sure wouldn't help it. Perhaps shutting down nutrient transport is one of the principal seconday effects. Anyway, on a practical note, I've hd pretty good luck tilling in grass that was still green after treatment with glyphosate, when I was in a hurry to get a site ready. The absorption is pretty fast, certainly less than a day, though it takes a while for the plant to go brown. Once the glyphosate is in the root system, it probably doesn't make much difference when you till the stuff under. On the other hand, what often happens is that I haven't gotten all the grass/plants with the first application, and they stay green, or new seeds sprout. If you wait, and spray again if new green shows up, you'll likely get more of the stuff that will eventually come up. When I've done the fast system, I usually was tilling in compost or something and planned to till at least one more time before planting because even the dead turf needs to be broken up well so it will decompose. Under those conditions, I was tilling under anything that remained or had sprouted after the treatment.
Bottom line: If there's no hurry, let it go brown and zap any new stuff before the final tilling.
Chuck