I mean...how do you define downturn?

If you mean recession, as defined by two consecutive quarters of dropping GDP - if GDP drops, stock markets drop. Not sure the directionality there, but the two are usually part and parcel.

If stock prices drop, it's a great time for acquisitions if you're sitting on cash.

I suspect any time stock markets drop sufficiently, you'll see increased M&A activity, regardless of whether it is prolonged enough to count as a recession.