Not really. PHEVs are usually one-and-a-half drivetrains at most. They're almost never as complicated as a separate BEV and ICE drivetrains would be individually.
They don't typically have a full transmission or CVT either. Taking the new hybrid Civic for example: it just has a basic planetary gearbox that handles forward, reverse and highway cruising.
Any time you're not at highway cruising speed, it's just in the normal position where the electric motor drives it (the engine only functions as a generator). It's effectively an electric car with a small, far under provisioned in Civic terms, engine that comes on to top the battery up sometimes if regen braking isn't enough.
At highway speeds, the gearbox has the engine drive. And since it's a less powerful engine, it will have better fuel economy than one that has to ever handle acceleration from a standstill.
And the whole thing weighs about 3200-3400lb, far less than any electric vehicle. So you're "lugging" around less.
