is this sentence correct? The new employees worked long hours, hoping doing so would advance their careers.

Answer 1

It's awkward having those two -ing verbs right next to each other. It would be better, too, to have that "hoping..." phrase closer to whoever/whatever it modifies ("employees" in this case). Try this:

Hoping to advance their careers, the new employees worked long hours.

Answer 2

Would this be a Ambiguous reference?

Answer 3

Yes, in the original sentence.