No, it is not okay to pull for the slow tank. And no, there is never a situation where it's acceptable.

The tank knows what they are capable of and comfortable with. All pulling extra will do is either piss off your tank or make them panic. In the case of the former, most pissed off tanks will just let the mob kill you. "You pull it, you tank it" is the general consensus.

In the case of the latter, the tank could lose control of the mobs altogether while they are panicking, and there's a good chance of a wipe.

If people are THAT impatient and inconsiderate that they can't let the tank pull at their own pace, then you have a choice: leave, offer friendly and non-aggressive advice, or attempt to kick the tank and wait for a new one.

The only objectively correct choice is offering friendly, non-aggressive advice. Leaving makes zero logical sense because you'd never get a new queue to pop and finish the dungeon before the "slow tank" finishes. Kicking the tank also makes zero logical sense, because it's guaranteed you'd spend more time waiting for a new tank to join than you would lose just working with the slow tank.