It would also firmly align them with the hereditary noble faction, which isn't happening
It would firmly align them with the idea of Knightly Orders, which is not quite the same thing. In particular, their support is going to be part of what gets the resurgent Noble Orders back up off the ground. Given their significant steps in the other direction, and the fact that "the knightly orders" issue
is their step back towards a more moderate/nuanced position, I think they could make it work.
I think the greater sticking point is going to be the one where the whole "knightly order" thing means making major decisions for your kids well before the kid in question has any say in the matter. I'm not going to say that it's
impossible, but it seems unlikely. Past that... well, it wouldn't really align them with the hereditary noble faction, but it would make it quite likely that the kid in question would be thus aligned, unless they managed to set up a knightly order of their own.
Now, the two of them have a lot of research power between them. If they really wanted to, they
could manage to figure out a new way of doing this thing, and then set up their own knightly order. At the same time, that's a lot of investment, and some potentially serious moral pitfalls, and... yeah. That's not really where their interests lie.
Unless you mean giving up their kid to an existing Order, which seems very very unlikely. Not sure the Orders would even accept that, with the risk that between a blood-based Ascender and another Ascender that keeps doing groundbreaking research might manage to reverse engineer something from their kid, as it's not like they're going to give up access to their kid.
My take on this is that they hold a dukedom, and they're ascenders coming off of a war in which they were an obvious and critical part of preserving the Empire. They have enough economic power and soft power that if they came out strongly enough in favor of the Knightly Orders, and invested enough in them personally, they
could reap the kind of payoff in gratitude that would have an order set up shop inside their dukedom, largely beholden to them, and thus willing to work with them that closely.
Thing is... they
don't care enough. They're enough in favor of it to go on the record saying that they support it and are in favor of it. There may be some minimal effort or outlay that they should make to indicate that, yes, they really really
do care about this, and it
does count. They're not opposed to making that minimal effort. That's primarily important because of the clear indication it makes that the issue is at least somewhat bipartisan - that there are important people who are opposed to the hereditary noble faction who also support this thing, and thus that "hand power to the hereditary nobles" is not the only thing that it is doing. Past that, though... it's a minor thing for them.