The major issue with packing a wet tent is mildew. If a tent is going to be used for a short trip and packed damp only occasionally, there may be no problem whatsoever. On the other hand, if it's an extended trip, drying the fabric completely is very important for the life of the tent. Wet tents get a sour smell that becomes permanent.
If you have a nice tent, taking 15-20 minutes midday once in a while to dry it out makes good sense.
George
SLO