No, because you can’t mathematically guarantee that pi contains long strings of predetermined patterns.
The 1.101001000100001… example by the other user was just that - an example. Their number is infinite, but never contains a 2. Pi is also infinite, but does it contain the number e to 100 digits of precision? Maybe. Maybe not. The point is, we don’t know and we can’t prove it either way (except finding it by accident).