This may not actually speed up queues at all.

What this would result in, is you entering multiple queues at once.
Not only would this strain the servers, everyone queuing with two classes would double the amount queuing at any one time, meaning queues would double in length. Three, four, five classes at once? You can see where this is heading?
Obviously 'queues' in the game don't work exactly like a real queue, but if there's any discrepancy in role allocation, which is what actually results in long queues in this game, that would only be amplified.