See https://en.wikipedia.org/wiki/Normal_number Answer: No one knows, but we assume Pi is normal.

Wow, your question led to some Wikipedia research on my end, and I found this:

'In particular, the popular claim "every string of numbers eventually occurs in π" has not been proven.'

I think I claimed this before. Oops!

Quote from https://en.m.wikipedia.org/wiki/Normal_number.

The probability that that's the case is 1, but that's not the same as a proof.

Not in digits of pi necessarily (needs a proof), but indeed in any truly random character sequence with independent probabilities of characters; you can easily calculate the probability of it, exponentially decreasing with number of characters in the desired sequence.