Yes. ASP.Net servers may have COM objects permanently registered. This kind of ability is usually used to bind other servers into the ASP.Net system (for example, one commonly sees this with special-use databases and device drivers for streaming hardware, like webcams for a multicast system or what have you.) Given that PrinceXML apparently has a COM implementation, you should be able to register the object using the same mechanism.
That said, if you need to install new server software, an option you might consider looking into is a virtual private server (starts around $10/mo) or a dedicated box (starts around $30/mo). In either case, you'd have root, and could install what you want. Running either of those with Windows is usually a price spike, but if all you need is a Prince server, it may still be the best option.
Because I sell hosting, I will not provide hosting links; it would be unethical. However, there are a bujillion hosts out there (most sell as VPS rather than the full phrase.) Just make sure they're telling you what your minimum bandwidth and minimum CPU time are, and you'll have weeded out 90% of the unsafe places on the spot.
John Haugeland is http://fullof.bs/