do you retain booster pack drop eligibility if you let go of dropped cards?

There is no real Loophole in it.

If you delete a Game only the License subscribtion is deleted.
Playtime, Achievements and so on are still stored in the System but not shown in your Library anymore.

If you activate the Game you deleted with a different Key again, you will get your previous License Subsription back, not a new one.
So you can´t activate a key, farm Cards, delete the Game and do it over again.

Hmm... maybe i misunderstood what loophole you are talking about, if it is not the above described Scenario.