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Of course, some games are in constant beta testing away from the main game, like MMOs.
Although to be honest our opinions are pretty moot, as it depends on the company giving you permission to test their game. Their game, their rules etc.
If you do go and test it, don't treat it as a free ride. You are there to do a job and I've seen plenty of people play a game, not report bugs and then complain when the game isn't available because they are patching it.
Generally they just want you to play the game. And report anything that you find wrong.
Did some "Alpha" testing once, and they gave me specific tests to carry out. Was fun.