The FANMADE_GUIDE says the following: "...you’ll be forced to on the second time (easter egg: if you keep clicking “don’t stop”, the options will eventually invert, just to mess with you ;p)." but with a bit of experimenting, I found out that it is possible to let the painting be completed by not disturbing Thane. If you keep on pressing the "let Thane go" option a few times after it inverts with the "stop Thane" option, you will eventually allow Thane to enter the cave and do his thing ... and when you come out of the painting, Thane's painting by the Dragon will be finished and not burned. :)
No idea if it impacts anything other than dialogue tho.