Not in football though. In fact, I think NESCAC specifically bars members from playing out-of-conference football games, and they may be the only NCAA conference that does this.
Anyway there is no room for any out-of-conference games. NESCAC has 10 football teams (the 11th member, Connecticut College, doesn’t play football). So each team has 9 in-conference opponents. But NESCAC only has an 8-game football schedule (probably the shortest in NCAA). So there isn’t even enough room in the schedule to play every in-conference team, much less out-of-conference teams.