I think I might have this down but I haven't been able to find a concrete definite yes.
Here is what I believe to be Time Vaults new errata:
Time Vault 2
Artifact
~this~ comes into play tapped.
~this~ doesn't untap during your untap step.
Skip your next turn: Untap ~this~ and put a time counter on it.

,Remove all time counters from ~this~: Take an extra turn after this one. Play this ability only if there's a time counter on ~this~. [Oracle 2001/08/24]
Because of the colon after "Skip your next turn", this by definition is an activating ability. Basically in order to put a counter on Time Vault I need to activate its cost, which is to skip a turn. Knowing this, I could then keep activating Time Vault and put an infinite number of counters on it thus makign my opponent take an infinite number of turns.
Is this correct? Is my reasoning correct?
Thanks in advance.