(1) Do statements about the future have truth values?
(2) Do irrealis statements have truth values?
Obviously, if the answer to (1) is yes and the answer to (2) is no, then future cannot logically be irrealis. However, there is good reason to say that future statements cannot have a truth value (or that they have a conditional truth value).
At the heart of the matter is what we mean when we say "John will arrive at 3:00 tomorrow". Is that truly a future tense statement? Is it the same as "John arrived at 3:00 yesterday"? One answer is no, that people mean "I believe John will arrive at 3:00 tomorrow", or "John is scheduled to arrive at 3:00 tomorrow". However, I firmly believe that in some statements from some people, there truly is a future tense. After all, we can negate the future: "It's not going to rain tomorrow". Conservatively, we can reduce that negative statement to a negative statement of belief, but I'm not convinced that's how we practically use the future (note that I'm not just talking about English here, but all langauges that have future marking that differs from irrealis marking). Logically, future is irrealis, but people don't speak logically. So taking a logical standpoint that when someone says "It's going to rain tomorrow" they cannot logically know the fact, that it is a statement of belief or prediction, is not necessarily valid or relevant.
If we compare the truth values for various irrealis contexts, we find that they differ significantly from the future. Conditional statements are evaluated by A --> B (I'm using --> to mean "then"), i.e., a conditional statement is true if A U B (U being the symbolic logical symbol for "and") or ~A (~ being the symbolic logical symbol for "not"). Counterfactuals have a similar truth value, but with the added given that A is not true, e.g., "If I had a million dollars, I'd be rich (but I don't have a million dollars)". Imperatives have no truth value: you can't say "that's not true" if I tell you to shut up (though you can respond that you are not talking, since imperatives presuppose that whatever state is demanded is not currently in existence, in this case, that you are not shutting up). Interrogatives I take to have a (vacuous) truth value, because if I say "Is it raining?" I am asserting that either it is raining or it is not, yielding an logical entailment of A v ~A (where v is the logical operator for "or"), which is always true.
On the other hand (to me, at least) future statements simply offer a single simple assertion: A, e.g., "It will rain tomorrow", and can easily be evaluated, even if not at the present moment. Likewise, past and present statements also give the simple assertion A, without any conditions or complex interactions. Since language and logic are so often not intertwined in any meaningful way, I haven't yet decided if this kind of analysis is at all useful, but it's a start.