As the name already suggests, truth conditional semantics is only interested in the truth of a statement, not so much in whether or not that statement makes sense pragmatically.
Form a truth-conditional perspective, the sentence "Colorless green ideas sleep furiously" is a syntactically well-formed sentence (not only a formula, but a sentence), and well-formed sentences by definition have a truth value as their extension.
Before we proceed, one should be careful about conflating the extension of an expression with its meaning. The extension of a sentence is its truth value in a particular situation; but few speakers would intuitively agree the the meaning of "The cat is on the mat" is just "1" (or "0"). The intension of a sentence is, under the classical formal semantic treatment, an abstraction over the sentence's possible truth values under different possible worlds, or equivalently, the set of all those possible scenarios in which the sentence becomes true. This idea comes closer to what is commonly understood as "meaning", but since the intension of an expression builds up on its extensions, it ist still useful to continue the discussion about truth value extensions here.
Truth-conditionally seen, the sentence is not meaning-less, because it does a truth condition: namely that it is true if and only if the situation it gets evaluated in fulfills the conditions that there is some x to which the predicate "idea" applies, and which is part of some sleeping event which takes place furiously, and so on.
The point is just that these theoretical truth conditions will never actually yield a true sentence, because, for example, the condition that our x is located in the intersection between "colorless" and "green" - which is obviously an empty set - will never be able to get satisfied.
Since there is no situation in which the sentence can become true, it would be dubbed semantically contradictory - but this still implies that it has a semantic value, namely "false" in all situations.
Strictly truth-conditionally, a sentence would only be nonsensical if it was syntactically not well-formed so the truth conditions which arise from a functional combination of the parts it is composed of cannot be formulated (like in your first example sentence, where you have a determiner + determiner + verb construction, for which there is no rule how to combine these types into a logical assertion under which the involved elements make a true sentence).
At the level of formulating such truth conditions from the individual elements and their syntactic structure, the logic is "blind" for issues like semantic incompatibility; as long as "ideas" is a noun that predicates some individuals which form the subject, "sleep" is a verb that applies to these individuals and so on, it is truth-conditionally meaningful in that we can formulate conditions (namely "= 1 iff there is some x such that Idea(x) and ...") under which the sentence becomes true.
Truth-conditional semantics has a rather narrow world view, in which everything - as long as it be a grammatical sentence - can either be true or false.
For example, the famous "King of France" problem:
Assume that there is no present king of France.
Is the sentence
The present king of France is bald
true, false, or nonsensical?
would by most truth-conditional semanticists be answered by "false", because the assumption is that the sentence can simply be transformed into the predicate logic formula
∃x((KoF(x) ∧ ∀y(KoF(y) → (y=x))) ∧ Bald(x))
"There is something which is the king of France (and for all other things that are also the king of France, this other thing is equivalent to the first individual, such that there really only one king of France), and this individual is bald"
which can simply be negated by negating the whole sentence
¬∃x((KoF(x) ∧ ∀y(KoF(y) → (y=x))) ∧ Bald(x))
"There is nothing which is the king of france and ..."
thereby negating the existence of such a king, which makes it a perfectly well-formed sentence with a truth value.
This would be the Russelian point of view - Frege (and I) would disagree and say that if the presupposition of a sentence (like that there exists a present king of France) is false, this sentence can neither be true nor false, because negating the sentence ("The king of France is not bald") would still exhibit the presupposition (in fact, that the logical entailment follows from both the affirmative and the negative sentence is the very definition of a presupposition! So under the account presented above, the sentence would have no presupposition at all, which I find simply implausible). But enough semanticists would say that the sentence is meaningful, truth-conditionally.
Long story short: Truth-conditionally seen, the sentence has a truth value due to being syntactically well-formed, which, however, will turn out to be false in all situations, because the truth conditions that there is an x which is both colorless and green etc. are inherently combined in such a way that they can never succeed to make the sentence true - but then the answer is just "false" rather than "nonsensical".
In order to get a more decent answer, you'd have to tune your semantics up quite a bit, for example with features. Then you can say that, for example, "sleep" is a predicate that can only apply to living entities (something like [+ LIVING]), a feature which ideas (being abstract entities) don't have, so the elements' types within the sentences don't match and then you can indeed say that the sentence is nonsensical rather than simply false.
But that requires a lot of complicated set-up and ontology and is not what is usually meant when talking about truth-conditional semantics.