Okay, I am not an Arminian. The point of this is to show that, even if everyone were to agree to determinism, it would not necessarily remove the arguments between Calvinists and Arminians, and thus things like the Wesleyan denomination would still have a reason to exist beyond adding to the total number of denominations.
I take the relevant difference in this debate to be, not that of whether or not we have free will, but that of who the active agent in salvation is. I also believe that this question an be separated from the free will debate. I am not planning on saying much else in this post.
A Calvinist will say that God is the active agent, causing us to have faith. An Arminian will say that God initiates, enabling us to have faith by prevenient grace, but that we must each finally choose to have faith in Christ.
The hard part is separating the agent question from the free will debate. Given determinism, God knows the future. He knows what will happen given any original state of the universe he might create, and, given his nature, what he will do in that universe and how that will affect things. Thus, God knows who will be saved and has a certain amount of control over who is saved. However, this is a different kind of control than the Calvinist ascribes to God. The Calvinist holds that God chooses each individual. What determinism entails is just that God can choose from a certain number of, likely restricted, sets of possible saved people, which set to actualize.
So, given determinism, an Arminian needs to hold that God chooses from a set of possible worlds, and in each possible world, a certain set of people are saved--which God knows even while choosing which world to actualize. God's choice is therefore limited by the nature of the individual persons. He may choose, again to a limited extent, which set of persons to actualize, but which of those persons comes to faith would then be reliant on the natures of those people and their circumstances.
I think this leaves a meaningful distinction between the God as active agent and the person as active agent in salvation. I also think that this is actually where the difference is problematic--even given determinism. I therefore also think that the free will debate is not really all that important to theology.