I don't think that the ENnies should actively prevent WotC from entering.
However, I think it's a more complex situation for WotC. I generally have a positive impression of WotC and the work they do, and I believe that they would want to win on the merits. To win the Ennie because they have the best product.
But the reality is that a WotC product is far more likely to be familiar to most people. And maybe that would end up with people voting for WotC because they've tried their product and not the other ones. WotC wins because it's the most popular, not because it's the best. I don't think WotC would be happy with that result.
The key question is how likely is the above result? If it is very likely, then WotC should refrain from entering. If it is not likely, than WotC should jump in gladly.
So I really don't know. Maybe WotC should only put up one or two books for consideration. I.e. its masterworks for that year. Like this year, put up Star Wars SAGA.