Strictly speaking, the title sentence is grammatical, but it sounds unidiomatic because there's no connection between the two predicates. Mother comes into the daughter's bedroom and says: 'Have you thanked Uncle Edward for that lovely present he gave you? It's now two weeks ago, you know.' Daughter says 'Please, not now, Mother. There are even contexts in which there is a perfectly good connection between the two statements in your example.

The disconnect is a logical rather than a syntactic one. So if someone says they are tired, we do not expect them to go on and say they are working. Being tired is associated with not wanting to work or not being able to work. There is no doubt about the grammar here. In the case of your example, you can see the grammaticality of it just by substituting but for and. This one is not exactly zeugma, but something rather like that. So the sentence jars and, as a result, can be funny. Here the zeugma involves the same word ( wrapped) first metaphorically and then literally. He walked into the kitchen wrapped in thought and a bath robe. For example, zeugma involves a kind of non-sequitur. There is nothing ungrammatical about this sentence.

I have started doing my homework