Given a grammatical sentence like "Colorless green grass sleeps furiously" is it possible to assign a truth value to it?
Only some sentences have truth values - those that do are called propositions. The given sentence isn't a proposition so one should not expect it to have truth-values.
Propositions are a small part of meaningful sentences. For example 'Hello, how are you?', 'that was wicked!' are meaningful sentences, but they aren't propositions. The sentence 'the invisible worm that flies through the howling storm' is meaningful in context, which is a poem by Blake - The Sick Rose - and here the 'Rose', is not just a Rose; but also England and/or perhaps Nature; to gather its full meaning one must engage in the the hermeneutics of intepretation taking account of Blakes ouevre and his influences.
But to go back to your sentence - or rather Chomskys; as he suggested it as an example of a gramatically correct sentence but that it lacks meaning; this is correct in one sense, but not in another; the meaning of this specific sentence is the one that Chomsky gave it:'grammatically correct but lacks meaning'; this appears as a reflexive contradiction - but the contradiction is only apparent; Chomskys notion of meaning is a narrow one - the one alluded to earlier; it would be an interesting study to specify just how narrow.