No, if you exceed the Droop quota you're guaranteed a number of seats regardless of the allocation system. So you can

1. exclude parties not making the threshold
   
2. allocate seats by full multiples of the droop quota
   
3. apply the d'Hondt method if there are any remaining seats unallocated
   

Step 2 just takes care of most of the initial steps of the d'Hondt method.

Can the last politician to go out the revolving door please turn the lights off?

The d'Hondt method uses the quotient of dividing the number of votes by the number of seats so far allocated, plus one. There is no double counting as the seats allocated by the droop quota are taken into account when applying the d'Hondt method.

Can the last politician to go out the revolving door please turn the lights off?