Any benefit in using Razz Berry and Great Ball at same time? Any harm?

Solution 1:

  1. Yes they are additive if used at the same time.

  2. There is no data on if using a Pokeball and missing causes them to run away faster after a failed catch.

More often than not, the reason for the run away is just the higher the cp and more difficult a capture is, the higher chance of running away seems to be.

Solution 2:

Yes, the effects are additive. This can be seen by tapping and holding on a Pokéball to see the color after throwing a razz berry, and then releasing it and switching to a great ball and doing the same thing. You will be able to see the difference in color of the ring change color (provided it wasn't green to start with).

source- personal experience