Truth, as I define it, is essentially a domain whose constituents are propositions that comport with observed reality. An unfalsifiable hypothesis can certainly comport with reality, but it cannot be a Scientific Theory for one simple reason:
Science is tentative.
Without tentativity, skepticism, and empiricism, the Scientific Method would be a useless tool. Take, for example, the following hypothesis:
There exist invisible, mass-less, extra-dimensional monkeys behind everyone's head.
This is an unfalsifiable hypothesis as any objection to it pertaining to the inability to perceive them can be shrugged off by claiming that they don't interact with the electromagnetic spectrum, Higgs field, or even the fourth dimension.
Now, in order for this to be true, it needs to comport with reality. The best way to do this is to draw proposed conclusions that would lead from the hypothesis.
If these invisible entities exist, then we should not see any monkeys behind our head.
This is a perfectly reasonable prediction based on the hypothesis; if there were invisible beings behind your head, you'd never be able to see them.
We do not observe monkeys behind our head.
This prediction was confirmed, right?
Of course not. Such an unsound foundation of epistemology inherently will lead to contradiction and the acceptance of wildly inaccurate claims. Even though we formed a hypothesis, made a prediction, and compared it to observed reality, we cannot say that it is "true" in the absolute sense. The difference between evidence for a Theory and proof of a claim is that evidence is merely some datum or data that coincides with that Theory. We can use the fact that we do not see monkeys behind our head as evidence of trans-dimensional feces-flinging primates, but it certainly isn't proof. Proof is similar to evidence in many aspects, except that it necessitates support for only one claim over every other claim that attempts to provide an explanation.
So, all in all, I'd say that an unfalsifiable hypothesis cannot, by any means, be considered to be apart of "absolute truth," since we'd have no way of confirming, proving, and most importantly, falsifying the claim.