Meh, I drove over 1000 miles pulling a loaded trailer, then several more months around town without mine hooked up, why? Because the wire burnt through on the redneck temporary exhaust while moving to Indiana from Phoenix.
Yes, the check engine light was on and most likely it used a bit more gas, but normal driving it did just fine.
Yes, still better to have it hooked, but absolute vital is a bit of a stretch.
Do what you can to get it working, mine is in some headers, nonheated, it acts up all the time, well, back when it was still running. :-P