I don't see why not, but the more common way of saying it would be to use "made" rather than "had."
"All the work made me exhausted by the end of the day."
"The movie had me getting bored, it wasn't very interesting."
This wording seems awkward. Most people would just say "the movie bored me."
On the other hand, saying "he made me laugh" is different from saying "he had me laughing" which tends to convey a prolonged state of affairs, as opposed to a single instance.