No, they handle playout and deliver 7flix to Seven as a channel. It still goes through BCM. Seven adds 7flix to their existing transmission of channels from that point, just like Racing.com or the defunct 4ME.
BCM not being able to do playout is the capacity and technical issue you mention.
It’s not just for 7flix, but it’s also being given a rest on 7mate, who airs it on Thursdays.
Considering that October was the month in which Seven acquired the rights to TBBT repeats back in 2015 (with S8 added on that same month in 2016), I wonder if the repeat rights are currently up for negotiation, hence why its not on the schedule for next week on both 7flix & 7mate?
I don’t think Seven will Fasttrack Grey’s Anatomy and How to get away with Murder this time around. Why? Free-to-Air Fasttracking from the U.S. is Dead and Streaming is the New Live.