I signed up for AGR about 4 weeks ago, and booked a trip for two weeks from now. My AGR card hasn't showed up yet. Will there be an issue on the train if my card doesn't show up?
No, in fact they won't even mail you your card these days until you've taken a trip. As long as you provided your number when making your reservation, you'll get the points for your trip regardless of whether or not you have your card.
The train crew does not care about AGR. If you have your number on the ticker or not, if you are on a reward ticket or not, if you have status or not they don't care as long as you have your ticket.
As long as your AGR number is attached to your reservation, that's all that matters. Most times you don't even need your AGR card. (Unless you're like Select+ and use it for Lounge access.) I have memorized my AGR number, so I can put it on my reservations. However, I have NO idea where my card is!