Thats exactly what I did, and the morrison went first go. Very slight rod knock but run reasonably well. One that I don't mind doing the side verge with all the tiny gum nuts on it with.
I have found that sometimes they don't prime due to the little spring, ball bearing and rubber washer falling out of one of the holes behind the primer.

I actually sometimes put the regular large whipper snipper primer bulbs (that fit zama and walbro) on these briggs, reusing the existing circular retaining washer. Came about when i ran out of the proper ones one day.
Seems to work just as well