So in my game, the players know about Rheingasse and found Drachenfels on their way to visit it.
I am generally going with a less than competent view of the Order (which is mostly filtered through my experience of academia). I see the Rhine tribunal cracking at the seem because of poor maintenance. The Divine and mundane are gaining on the magical realm, there are fewer and fewer vis sources going around, and the older magi who can just overrule the young are still enjoying the fat of the land. I have also deliberately describe all the mage meeting place they visited like the professors' offices that I've known: big, messy, chaotic, with old piles of (unread) papers everywhere, frozen in their comfort zone.
I started the campaign in 1221 after the Tribunal which officially re-opened the Rhine, but with Cintera having "used the nuclear option" and veto'd the officialisation of Heorot (I'm going with the Cintera schism in the background since no PC is Bjornaer, and the only thing that temporarily unites wilderists and Harmonists is a visible tangible external enemy).
I plan on having Rheingasse show them this. The Rheingasse would be the mouthpiece of Stentorius who would like to recruit the new group as a way of growing Fengheld and to effectively weaken Murion, with a possible view on Fengheld becoming the supreme Covenant in the Rhine. Weiss will also mention that Cintera is just waiting a few more years to bring vagrancy charges against the Heorot people (as a way of deflecting internal anger towards an external source).
Similarly, Daria la Grise wants to make the new party Triamore's chapter house as a way of extending her influence and gaining actual votes (with her own held by Stentorius) as well as magi to help restart Lotharingia, and who'd dangle giving them full Covenant-hood once the Lotharingian Tribunal is formed. I like the idea of Daria already having machinations, and looking for ways to get out from underneath Stentorius' heavy thumb.
Note: I have not read the Triamore setting book, so I'm just working from scratch for it. I have decided that Gracchus ex Veriditius was the top Verditius in the Rhine and based there, but reached the point where he could no longer make longevity potions for himself (an idea taken from an ex Misc in the Provencal Tribunal), and so Daria ended up seeing that leadership of Triamore (and a lot of free necromantic stuff) was heading her way as he started rapidly wasting away. This gave her time to get ambitious.
Nonetheless, while Fengheld and Triamore would prefer the party to become their vassals, forming an independant covenant is possible, since Waddenzee (one of the PC's apprenticeship Covenant) and Dunremar are instantly on side, and most other Covenants simply not caring enough to block it (what would Rozhov and Irencilla gain or lose with something happening on the opposite site of the Rhine). The only ones that will be against will be Dankmar, just to spite Dunremar rather than for a good reason.
I am going with a strong theme of conflict with the campaign, and I think that this would reinforce it. But overall, the Fengheld "clash" is a plot hook more than a reason not to go there.