I'd say, after consulting with the OB/GYN to make sure what you take is on the safe list, the biggest problem would be whether the cough drop smell or taste might trigger nausea.
It's a fact that pregnancy can change the way a woman smells or tastes familiar things, and I would think, since cough drops usually have a strong flavor or smell, that pregnancy might affect how these come across to a pregnant woman.
I'd try something like Riccola or similar, since these usually aren't quite as strong. And I’d start with a fruit flavor, like cherry. Might go down a little easier.