Yes, you can do that. Activating any regeneration ability only sets up a "shield" that lasts until the end of the turn (cleanup step to be exact) or until it is used up to replace a destruction event. You can do that even if such an event is not imminent, because the game does not look into the future to see what might happen.
Yes. You will create 20 Regeneration "Shields" which may or may not be used up. Whether they are used is irrelevant for whether you are allowed to activate the ability though.
In general, you can activate an activated ability without targets as often as you can pay its cost, regardless of what the ability would do when it resolves (C.R. 118.3; but see C.R. 602.2, 601.2b, 601.2c). (This applies to Dark Privilege's activated ability just as it does to, say, Nantuko Husk's.) Thus, for example, you can activate Dark Privilege's activated ability 20 times by sacrificing that many creatures to pay the cost.
EDIT (Feb. 18, 2020): Correctness edit. One rule was renumbered with Core Set 2020.
In other words, if I don't care about or need the regeneration effect, can I still sacrifice as much as I want?
Thanks
Former Rules Advisor
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(The Gamers: Dorkness Rising)
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EDIT (Feb. 18, 2020): Correctness edit. One rule was renumbered with Core Set 2020.