It depends on the individual entirely in your hypothetical question. Usually though, as another poster stated, possessing offensive grappling ability with striking will reduce a single-dimensional (limited) striker's effectiveness. But, it depends on who they are.
Conor isn't affected too much by the TDD threat because he's got really good control of distance and is a very good scrambler and because he doesn't allow it to impact his striking's effectiveness as much because he blocks it out. It's a mental thing. The consequences of blocking it out entirely could lead to ending up on your back after throwing, whether you land or not, and potentially not being able to get back up, taking a beating, and/or being finished.