I then set up Extended Events to capture the query metrics and I executed each of the queries multiple times (also, just for the test, I discarded the results because I didn’t want that process mucking with my measurements). After executing both procedures 500 times, the results were quite simple. The average execution time with an explicit drop was 8,672 microseconds. Meanwhile, the average for not dropping the temporary table was 8,530 microseconds. That’s about a 1% difference across hundreds of executions. Reads were identical and so were writes.
In short, the behavior is the same.
What about the impact on the system? Could I see changes in memory or I/O as these different processes ran?
Grant didn’t notice any difference but check Allen White and Jay Robinson’s answers in the comments. Temp table reuse can happen (if you follow the rules) and can make a difference when a procedure is called frequently enough.