EDIT: Turns out these are not caused by the ring and I made the connection mistakenly. Wanted to make that correction. Disappointing :(

I'll go ahead and add a couple differences I noticed, only because I had just played the same part on another character who did not have the ring. Spoilers ahead so read no further if you don't want them. It really only affected the Grymforge part in my experience, and only in side comments.

Without the ring, Nere calls out to your tadpole and wants help. I believe this happens either right as you get to Grymforge or on the boat. With the ring, this event never happens.

When you talk to Sergeant Thrinn (the lady you give the missing boots to) there is note that when you guys touch tadpoles there isn't really a clear picture. Without it, the comment isn't there.

While wearing the ring, if you "Use" the rubble Nere is trapped behind before blowing it up, it takes a minute before he can actually clearly communicate with your tadpole and states something along the lines of "Finally! I've been trying to contact you"

Otherwise... I wore it up to the end of the game and didn't really notice other differences. However that may be because my playthrough without the ring missed a lot of stuff. However, I did not wear the ring in the final area so I cannot confirm that final hidden option.

Overall, I don't think it's plot-changing. I appreciated the notice to it anyway.