I don't speak from position of knowledge or authority on this, just my own reasoning, which may be flawed.
I don't know whether fitting tyres to roll with the directional arrow has any effect on performance or not, but I always fit my tyres so that they face that direction, it's probably down to OCD more than anything else, which probably also explains why I could never just flip the wheel round as
@youngoldbloke suggests, no way, the tyre would have to come off and be put back on facing the correct way.
A couple of things that occurred to me whilst reading this thread, were: firstly, if tread does not dispel water, why do tyre manufacturers bother with it? Surely they could reduce costs by eliminating the part of the production process where tread is put on the tyre? Secondly, as for aquaplaning, is it not the case that bikes don't aquaplane because they don't go fast enough for the tread's effect to be overwhelmed in the same way that causes cars to aquaplane when the vehicle goes so fast that the tread can no longer dispel water quickly enough? If that is so, perhaps tread on bike tyres is actually doing its job>
Also, if tread is as ineffective, and superfluous as some suggest (if I get their meaning correct), why do people complain that some tyres make riding your bike like cycling through treacle (Schwalbe M+ have been cited to me as having such a characteristic)?