The G is nowhere close to its maximum capacity: It currently only runs 1/2 length trains, and the frequency is much less than what could be supported if there were more demand. Even during the L train shutdown the G should be fine as long as the MTA increases service appropriately, which they have stated they will do.
The real chokepoints for the G will be the transfers to Manhattan-bound trains: to the E at Court Square and to the A/C at Hoyt-Schermerhorn. Those stations will be way overloaded, and the MTA hasn't announced anything that would mitigate this significantly.
However, Amazon-bound commuters shouldn't contribute significantly to this, since they will be exiting the station at Court Square, not transferring. Workers commuting in on the E/M from deeper in Queens might have some issues getting off the train in a very crowded station, but at least they won't be contributing to the capacity problem on the way to Manhattan.