If it runs as a purely web-based system (like any other website, just PHP or Perl code), it ought to be OK (unless you get so popular as to overload the server!). I just took a quick look at the Mercurial page (www.selenic.com/mercurial/) and I see references to its "binaries". That could be trouble, if the Linux version isn't compiled and linked to work with exactly the Linux level provided on LP servers. It also makes use of "mod_python" -- better check if that is available (apparently not, as of this June). If you can spring for a VPS or dedicated server, you could possibly install Mercurial's prerequisites and compile it on that server. Otherwise, if you want to stay on a shared server, I think you'll probably need to find something else.

As for your need for a distributed source control system, I take it that you're planning to host a collaborative code development effort? Something like Sourceforge, but on a much smaller scale? If it's something else, such as text production, perhaps another development model would work (e.g., a wiki or a CMS)?