Does tread make that much difference when commuting in the wet? No

It's the compound, not the tread that interfaces with the pavement. Because of the rounded shape of a bicycle tire, they simply aren't able to hydroplane at speeds that are attainable on a bicycle, and, if you are going that fast, your tires are going to be far down the list of things to be concerned about.

Sheldon Brown (RIP) was one of the most respected voices regarding all things bicycle. Here is what he had to say about tread features on bicycle tires:

Tread for on-road use
Bicycle tires for on-road use have no need of any sort of tread features; in fact, the best road tires are perfectly smooth, with no tread at all!
Unfortunately, most people assume that a smooth tire will be slippery, so this type of tire is difficult to sell to unsophisticated cyclists. Most tire makers cater to this by putting a very fine pattern on their tires, mainly for cosmetic and marketing reasons. If you examine a section of asphalt or concrete, you'll see that the texture of the road itself is much "knobbier" than the tread features of a good-quality road tire. Since the tire is flexible, even a slick tire deforms as it comes into contact with the pavement, acquiring the shape of the pavement texture, only while in contact with the road.
People ask, "But don't slick tires get slippery on wet roads, or worse yet, wet metal features such as expansion joints, paint stripes, or railroad tracks?" The answer is, yes, they do. So do tires with tread. All tires are slippery in these conditions. Tread features make no improvement in this.

If you want to read the entire article on bicycle tires, you'll find that here: http://www.sheldonbrown.com/tires.html

The total irony here is, our wet weather road racing tire has a very subtle tread pattern, and my initial reaction when we got them was (WTH??? or some other consonant). We even state somewhere in our literature that "slicks" grip better than tread feature tires. So, at Interbike I asked the person in charge of such things (they come over every year from Germany to see how we do it here) point blank, "Wha?". The response mirrored almost to a word what Sheldon Brown said, that the tire wouldn't sell very well without the tread pattern, and that it would technically be a better tire if it didn't have them. Now, the tread pattern is very subtle and the difference is too small to really make a difference, but even out tire engineers, succumb to market pressures. We are in the business of selling tires after all.