Shall I undercut the drywall to let the baseboard cover the hardwood floor expansion gap?
1/2 expansion gap total gives you 1/4 on each side, which should be easily covered by the moulding.

That said, yes you absolutely can trim the drywall to allow the wood floor to expand. An engineered floor, though, likely doesn't need more than 1/4" on each side. It should be dimensionally stable.