The Mechanicus would also be horrified at the Breaking Yards. They see a noble and ancient Raider getting ripped in half and broken down into its component parts so that it can be sold off wholesale and they would have a case of the techno-vapors. They'd probably tear the whole thing down and label the whole thing tainted, completely blind to their own hypocrisy.
Also from the books I've read, most of them regard ship building and maintenance as something that they unfortunately have to do as part of their alliance with the Imperium, but they'd rather be out among the stars
committing horrible acts of heresydiscovering lost archeotech, and would hate to be stuck in one place waiting for someone else to bring them their leftovers for repair and scrap.
The terms our group agreed to (and through RP, actually my character) is that we'd help with the set up of an outpost in a trade centre.
Damaris, apparently, won't count as there's a Mechanicus presence there already. A shipyard... that will give them a base of operations to dock and take on assets, and while the scrapyard is probably abhorrent to them, probably considering it mutilation of divine voidships, it may be sold to them on that ground. Hey, let's take over this shipyard and you can stop these innocent voidships from being chopped up!
Or most likely not.
Still, even without Mechanicus involvement, what do you think about the Breaking Yards? It's not too much of a stretch to circulate that the yards recovered some archeotech weapon, or a big ship or something, that might be too tempting for the greenskins to surrender.
Hell, do I really even need to invest if all I want to do is get the Orks to kill themselves as they charge to SR-651?