No. How would I change the tube? I would have to walk back to my car, find a tube (I always bring one in my car in case of pre race issues) and change it there. That would be at least 3 laps, more likely 5. Or more depending on the crit.
Back as a cat 5 I did a training crit and I did bring my spare. Flatted and changed the tube in a couple laps. Didn't even try and get back in. Afterwards they were all "its a training crit, you could have just jumped back in". Made sense for a training crit I guess but didn't even consider it. As a cat 2 tho, no way.