Indeed you still can go South on SR37, however they're warning you that traffic can and usually does backup through the construction zone and will delay you an extra 10-25 minutes or so. It's usually not too horrible, but can be annoying at times especially if in a hurry.

Typically during Rush Hour (From about 4:30 thru 6pm-ish) traffic tends to back up from Victor Pike all the way towards Tapp (The red-light after the 2nd Street Exit Ramp). It varies day-to-day and the exact timing (tends to be worse from 5-5:30).

Honestly going through town during Rush Hour time, particularly with a trailer, is also a bit of a hassle as well. But thankfully you'd be going North to South. It's so much easier going either of those directions in Bloomington than it is East or West. And then there's those things called Red Lights that seem to never fall your way...

Still, as they said, those coming from the North should expect some delays and leave 10-30 minutes earlier. And of course keep an eye on changing Construction traffic as it moves North during the year and adjust accordingly. As of right now though it's not too horrible.

Safe Travels!