Hi, I've had a towbar on a W210 and on a Volvo, parktronic did not get
confused on either one (even when the detachable towbar is in place). But I
would still put a detachable towbar (had one on both).

Of course once you start towing something, you easily get an alarm. The
official electrical connections are done in a way that the rear parktronic
gets deactivated when you tow something, my car was not wired that way which
I think was good, it is easy to forget that you have something at the back
and once you put on reverse, you get an immediate alarm (but can switch it
off, from the parktronic switch, if you prefer so).

The rear parktronic system on the MB only turns on when you shift into reverse.

Tell me you don't plan on backing up with a towbar!!!