Considering the webway IS eldar/old one in origin, and that the Secret Project involved digging into the webway to adapt it for Imperial use. So no, the Emperor would not have any hangups against it.
I saw this lore bit a while back with the reveal of the Skitarii army, and it clearly sounds to me that the Mechanicum have managed to get access to the webway. Perhaps a smaller and unbroken conduit, apart from the main branch that Magnus shattered in his hubris. I paid note to the exhubris portal, which I believe is related to Magnus' folly
Sending a warhost through it to strike a deal with the dark eldar, whom retains the most of the eldar pre-fall knowledge in order to surely repair the ruined Imperial Webway I believe. Which would free the Master of Mankind from having to constantly expend all his power to keep the warp rift closed, and allowing him to heal.
That the warhost is Xanthite is also a curious mention. But it makes sense, if warpdabbling inqusitors have taken it upon themselves to try solve the issues of the failing golden throne before its too late. Where I daresay that other inqusitorial orders would more like to try to sweep the evidence in under the rug, praying for it to go away, or simply ignoring or denouncing it as heresy. The god emperor is infallible!