I could think up some issues, I mean for example strained or extra muscular fingers are not uncommon if using the DS phat, and you also need to have a strong lamp so that you can see the screen. Otherwise you can get trouble with your eyes.
Hardware-wise I'm pretty sure that the G6 lite works exactly the same on the fat one as on the slim I-did-not-eat-enough-porridge-during-my-childhood DS.
My bro has a DS Phat and a G6 Lite and he has not had any issues with it thus far. I have a DS Lite and a G6 Lite and it operates exactly the same as his. When he first got it, we had a bit of trouble trying to figure out how to get it secured properly in the GBA case, but after I saw a pic online of the way it's supposed to fit, it went in fine. Overall, he has not had any issues and the casing fits perfectly!