Theoretically? Citation needed. I believe this is only true if pi is normal, and while there's a lot of conjecture that pi is normal and no evidence that suggests it isn't, there is no proof.
Of course this begs the question of whether a number normal over an infinite sequence can contain sub-sequences that are non-normal - sequences of 100 tails will occur in sufficiently large completely normal (randomized) sequences of random coin tosses, e.g.
If this is correct, then you are correct, the conjecture would hold if pi were normal. But then wouldn't an FSG be able to succeed on the sub-sequence? Of is that acceptable, provided that the FSG fails on the overall sequence?
>>All that is needed for every work to appear is that each digit occur at least once.
Counter example would be a=0,123456789010011000111000011110000011111....
3.0140015900026530000....