SHERRY: So we’ll swing by around six?
RORY: Oh, sounds good.
The debate at Chilton started at 3.30 pm, and presumably finished no earlier than 4.05 pm, the end of the school day. Lorelai and Rory talked to Christopher and Sherry after the debate, and then they had a half-hour drive back to Stars Hollow. Say they got home at 4.45 pm, and have entertained Christopher and Sherry for about half an hour, it should be around 5.15 pm by now. Christopher and Sherry now have 45 minutes to drive back to Litchfield, get ready to go out, then drive back to Stars Hollow. Assuming a 20 minute travel time between Litchfield and Stars Hollow (the distance between Litchfield and Waterbury, and Litchfield and Washington Depot), they have only five minutes to get ready before getting back in the car.
It is very, very tight, but unlike other fantasy timescales in Gilmore Girls, this one is actually doable. Just.