It would depend on the version of Tetris you play.
Many versions now have a grouped random system. At the start of the game, it randomly arranges the seven possible shapes, and gives you them in that order. Then it randomizes the second shapes again starting on t he 8th drop and once again gives you one copy of each of the seven shapes in that new random order. Repeat every 7 drops.
This makes it impossible to get a single shape more than twice in a row (as last piece of one set and first of the next is the only way to ever see a double identical in a row). In any given chunk of 7 you may have a few duplicates if you have 3 from one set and 4 from the other. But you will never wait longer than 13 moves to get a specific piece you want (had it as first of one set, want another, but it was placed at last of next set).
If you played an infinite game on a true random version… then yes eventually you would get an insanely long chain of a single piece, because when dealing with infinity everything that is at all possible WILL happen eventually.
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