I’m of the mind Artoo has the plans before the Tantive is captured. They certainly can’t be on the “ATM card” Leia is putting in him. I think all she’s doing at that point is recording the message and giving Artoo his marching orders.
Also keep in mind when they get to Yavin, they hook up Artoo to a large unit to do essentially a data dump. That looks like something that would take a little time to do.