Canon, at least, do not change the voltage or clock up/down the processor(s), regardless of battery used. 1D, 5D, 6D, 7D, 80D, whatever. No Canon body has ever had variable voltage or clock based on battery power or grip.
Other companies, however do use this. Fuji, for instance, have a 'boost' switch on the grip for the X-T2 which does exactly this; raise the voltage, raise the processor back to stock speed (it's actually underclocked by default), and get higher performance. When you turn the boost switch off, everything returns to normal, despite still having two batteries.
Canon 1Ds already run with higher voltage and higher clock than all other Canon bodies. This is why 1D and 5D bodies of the same generation, with the same processors and both of a 'pro' level, still have a difference in base operation speed. The general rule with DSLRs is you underclock the processor(s) to keep heat down and keep performance consistent; the 1D bodies, exclusively, run their processors at full speed.
All that said, whether you use a grip or not is entirely personal preference. I always do, purely because even when holding the camera landscape, I find a bare 5D or smaller body too small. My fingers dangle off the bottom and it's genuinely distracting, to me, as someone who grew up on large format, medium format, and 1D bodies. Of course, plenty of other people want their camera bodies to get smaller and smaller...
It's entirely personal preference. There's no performance difference. Either you like the feel of it or you don't, that simple. You won't know until you try it; if your local store own't let you try the grip on your body before you buy it, ask if they have a 1D body you can pick up to see if you like the feel of that, since it's essentially the same.
