Hardly! Tests show it averages to about 3 to 6 minutes saved per charge. You can get the same results by charging with the phone powered off. Airplane mode is slightly better though.
I charged my iPhone when it's on and sometimes when it's off, and I've done that with all of them over the years. I've yet to notice any negative effects from doing so. Now, to answer your question, the answer is "it doesn't matter" if the phone is on or off during charging times.