No. Quantize does not affect the timing of your manually activated Cue. Quantize is keeping loops in sync, if I understand correctly.
You will need to make a quick correction on the jog wheel to fix your mistimed Cue.
I do think this would be a brilliant addition to the CDJ-2000 functionality, however. Perhaps the mods can pass along to the engineers for either a future firmware update, or a future model improvement?