Correct. Essentially, if you were to start from today, rank 15 of the cloak (Max rank before you start upgrading just it’s corruption resistance) would take 10 total weeks, including this week.
If you were to start on the week that rank 15 becomes available, you could achieve rank 15 within 3 weeks (or 2 if you really put your nose to the grindstone). There is technically an unlimited supply of the currency needed to enter the Heroic Visions, it’s just that your major sources are from Assaults and the daily Minor Visions. Outside of this, you must gather incrementally small amounts (5, 15, 25) to get another 10k currency.
EDIT: For anyone that might see this later, I’m updating with my new understanding of the system after a week. The catch, while it presents you the opportunity to have all the quests available, won’t necessarily allow you to catapult all the way up to 15 in 3 weeks. While it provide you with more access to the earlier levels, you will hit multiple points along the progression of the Cloak where you will have to run more than 1 Vision to get the necessary items to complete your upgrade quest.
In reality, this means that you won’t actually be able to catch up much once you reach these points (as some could potentially take 3-5 runs from what I’m seeing). There are times where you could get a slight bit ahead thanks to the catchup (say an upgrade quest takes 2 runs, you could start on the next one with your 3rd vessel).