Someone answer my question please.
Unlikely.
See, even if the tradition plays a great role in medieval christianity (as nowadays, you would say), mysticism was seen as dangerousy close to heterodoxy and once you have an united church with a clear institutional leader...Let's say it would be hard to promote something believed to have a damaging role.
Now, the best period to introduce such feature is maybe the Late Antiquity and having lasting, dominant regionally, heresies. Of course, it would prevent the constitution of A christian church, as we would be more in favour of increasignly "national" ones.
And, of course, Protestants or even the concept of western/eastern christianities are likely to be butterflied away.
I would point that depsite kings in a first time, then pope after 850/900 AD could say about mysiticsm, it was quite common in the everyday faith and religious tales. So it's less about mysiticm being "allowed to thrive" (something that makes little sense) but about popular religiousity being institutionalised.
And this latter, as said, is greatly unlikely.