The only thing I can think of is that the launcher is kept in RAM, and a less resource heavy launcher would free up available ram. That's a stretch though, and I can't say you'd notice that in something like selecting text.
This is the only thing that can affect other apps. If the built-in launcher never leaves RAM, it could affect performance elsewhere.
Launchers are just another app, they can and should be cleared from RAM when not needed. At the same time, launchers getting booted from RAM leads to re-draws when you do go back to them, and a bloated and/or inefficient launcher will make this a very annoying process.
I've had plenty of launchers back in the Froyo/Gingerbread days, and a lightweight launcher could make the rest of the phone appear to work better.
But I'm more with Slithery, the hardware should more than compensate for this, unless the device is old and/or super low end.