Depends on the price to be honest I won't pay 30$ for closed beta access (unless it's alpha or F&F) ,but I would pay yes and your post is 100% correct it will help the development and actually might increase the rate of the completion of the game.
That is why they do a beta to test things nothing is perfect and I don't know about Diablo beta ,but WoW beta has a feedback system ingame and you can post about almost anything even after you do a quest to.
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