One time a few years back, I did pretty similar to the bolded section above with at least fair to good results. I broadcast brassica seeds into still standing, but medium height(calf to knee high let's say) grass. (I had mowed it a week or two earlier.) So I spread the seed, then mowed, then sprayed and it worked halfway decent. But...there was not a heavy layer of duff/thatch present when I spread the seed into the standing grass. I remember thinking that the soil was fairly bare underneath the over growth.
So, in that scenario, I feel confident saying that a lot of the seed made it to the soil, which was largely bare. When I then mowed it, I created thatch, and plenty of it, but the seed was already on the soil below. It wasn't the prettiest looking patch, but it definitely fed deer that year. Back to your sequence...I would say it would depend on how dense the standing(after having been sprayed) weeds would have been. If so dense as to block the seed from getting through from above, then I think there would be disappointment/seeding failure. However, if the tiny seeds can make it down to the soil, I think that would be fine, even good to very good.
I have also in the past used spring planted buckwheat to suppress weeds/grass, prepare for later in the summer brassica seeding and feed whatever deer/turkey/bees/etc with the buckwheat and I think that is about the ideal "prep" planting for a later that summer no till brassica seeding. Buckwheat is cheap and easy to grow, helps the soil, etc, and is naturally dying off just about when you would want to broadcast your brassicas...AND...the structure of buckwheat plant is such that there is a lot of bare ground underneath those plants and the duff created by mowing it down over your brassica seed is much less than whatever grass and weeds come up on their own. I am trying to get better at no till, still without a no till drill that is, and I know I am planning on using the buckwheat strategy again next year.
