Can appearing research Pokemon retreat?

I've heard that the special field research Pokemon appearing (Mew) can't retreat so everyone will get it. How about the field research Pokemon? So far I've catched all from my field research tasks and breakthrough Pokemon appearing rewards. The reason I'm asking this is that if the reward Pokemon will always be catched, then a player would want to save berries and better balls and just use normal pokeballs.

Solution 1:

I used upwards of 20 normal balls to catch a Moltres after completing Field Research, and it never ran. This experience & the fact that the special research reward tells me that it won't run away.

It would certainly be a bad experience if it could run! Work for a week or more to catch a 'mon then it runs after a few balls?