Is a tank-style water heater always under pressure?
Yes, the tank is under pressure from the incoming cold water supply. After all, the incoming cold water is what is pushing hot water out of the tank and into your faucet.

However, there are usually two safety valves:


Temperature/pressure relief valve that will let the hot water or steam out, if internal pressure or temperature goes over a certain limit.
A vacuum breaker valve that will let air in if internal pressure is less than external (air) pressure: prevents the tank from collapsing if there is no cold water coming in and you're pumping hot water out.