No. A member can go on vacation but vacation time is limited and they will eventually run out.
As soon as a player goes on vacation, 24 hours is removed from their available pool. If they come back in 23 hours, 1 hour gets added back to their clock, since the were already docked that time. If they use less of the time then the difference between 24 hours and the time used gets added, up to the time control.
Can someone pause a game indefinitely?