You mean because the entire known sequence is finite, and every finite sequence occurs in pi infinitely often?

This is suspected but currently not yet proven.

In fact, we don't even have a proof yet that the digit 7 occurs infinitely often in pi. (Same for any other digit.) Right now it's conceivable, but very unlikely, that there is some final 7 in pi.

I suspect not. Pi is known to be irrational, and repeating sequences are known to be rational. So pi cannot be truely repeating.