The rope will have already dropped at least 15 minutes before your arrival.
There is a truism of AM EMH that says that if you want to get the most out of an (already too short) EMH, guests are wise to arrive well before the AM EMH opens, and then head, with well-planned determination, to the first 2-3 rides of the day.
You're, of course, not breaking any "rules" arriving deep into AM EMH, but you will be losing
a great part of the ADVANTAGE of the (again, far too short) extra EMH time.
By 8:15, you will likely still be able to ride TSM, but you will be behind thousands (yes, thousands) of other guests who arrived before 8AM (and continuing into the 8:00 hour,)
and headed directly to that attraction.