I cannot see the Imperials making the Tribunal part of their saints. The Cult is as much their to provide a place of worship for the colonists as it is to convert the natives, so they would likely have a hard time selling this change to their own. As for the Dunmer ancestor worship already has a head start on the Imperial Religion, not only because it was how they use to worship before the Tribunal, but also because the Tribunal essentially just built on top of this, they were still worshiping ancestors in the Tribunal Temple. I highly doubt that Dunmer who have been worshiping their ancestors for ages will simply stop and pick up the religion of the foreigners that having been occupying them. Sure, some will, especially with less fear of being labeled heretics and prosecuted by the Temple Ordinators, but I think almost all will simply revert to the old ways, which is really just doing what they always have done, but instead of worshiping the Tribunal as gods they would be seen as greater ancestors like the Daedra. Because of this the Cult really doesn't stand a chance at converting them, and so I doubt they will risk alienating their own. They will simply keep it as is, and eventually hope to over come the native worship because there might be a lack of organization to it now.
I'm sure there were several Dunmer in the Imperial City during the Apotheosis of Martin Septim.
It's not an unrealistic stretch to assume they bring the "good news" back to Vvardenfell. The news would spread there over time naturally even if no Dunmer from Morrowind were present. (I'm sure considering the size of Imperial City that some citizen of the Empire who witnessed it would eventually travel to Morrowind and tell the tale.)
The whole thing about the Tribunal being used as Church Saints by proselytizers in Morrowind is a bit of a stretch, I know, but it's not entirely impossible that certain chaplains and preachers representing the Church would try to at least draw some moral parallels between the Tribunal and the Saints of the Nine Divines. It's a very common real-life tactic for gaining converts. Christianity, one of the major world religions, borrowed many, many symbols, rituals, holidays and yes even Saints and Patriarch figures from previous popular "pagan" religions. If a Church is in the business of gaining converts and spreading its influence, and I have no reason to assume the Nine Divines Church is any different, then it would be most fruitful for them to appeal to pre-existing Dunmer culture in any way that doesn't overtly conflict with the basic beliefs of the Church.