* Technically: A sentence made of nonsense words will follow the grammatical rules of the language it's in. It might have a subject, verb, object, etc.
* Meaningfully: The meaning will be nonsensical because the words themselves have no established definitions.
Therefore, the answer is:
* True (grammatically), False (meaningfully)
Example:
"The blimpish flibbertigibbet quizzled the blargle with a snozzcumber."
This sentence has a subject (flibbertigibbet), verb (quizzled), object (blargle), and prepositional phrase (with a snozzcumber). It's grammatically correct, but it has no real meaning.