Would Xykon recruit Tarquin? I suspect the answer is"yes" - Xykon was happy enough to recruit Tsukiko and probably enjoys the thought of Redcloak having a rival.
Would Tarquin sign up? My guess is "yes, but only on a temporary basis". To join Xykon for a while, because he's too powerful to say no to and because it might be fun, is one thing. To permanently subordinate himself wouldn't be acceptable.
Tarquin versus Redcloak, while both are employed by Xykon, would be an interesting political battle, though perhaps too much of a repeat of Tsukiko versus Redcloak.