I really don't feel like adding strikes changes my ground strategy too much. Of course, it might just be my outlook on things because I don't find too much of a difference between gi and no gi either, etc. There are differences obviously, but I think the similarities are much greater.
In some ways, striking makes it a lot easier to grapple. People trying to strike you tend to leave more space which creates more openings to attack. In other ways, striking makes it harder to grapple because you simply cannot rest from certain positions the way you can in pure grappling (guard positions come to mind, particularly the half guard).
For the past few years I have only been able to train MMA infrequently, but when I do get to train with the fighters I tend to give a good account of myself in sparring. I will usually be able to control the ground part of training through my experience in BJJ. I am not as familiar with some of the trickier ways to trap and strike an opponent as MMA guys are, but I don't seem to have a problem getting to good positions and striking from there.
It's important to train with strikes some of the time, but I don't think it really changes the grappling strategy anywhere near as much as people make it seem.