Some accumulators have a manual valve on the outlet and some have a solenoid valve. If the valve is open when you shut the engine off, then yes it'll dump into the pan. However, when you restart the engine, the accumulator will refill with that 3 quarts. The extra oil in the pan, without the engine running, shouldn't matter.
A buddy of mine has one with a solenoid valve. He just turns it off before engine shutdown so he can use it to prime on next cold start.