I had a field last year that was pretty over grown and I just ran out of time to prep it ahead of time...so I broadcast brassica into the standing weeds, some of which were 5' tall, and then mowed it. My thinking was that I would get more seed to hit the ground broadcasting into standing weeds than I would if I mowed it first and then had the seed getting stopped by the mat of dead weeds.
Seeding first and then mowing worked out pretty well. Brassicas are small enough seeds that you can get some decent germination without tilling. Yes, there are better ways...but broadcasting it onto unworked soil can work fairly well.