Is it possible to use PyQt from IronPython? 
From what I've read IronPython should work with CPython compatible libraries but out of the box it doesn't seem to work.
If it is possible, will code completion work?
Hope someone else who spent more time messing around with this comes by and gives you qualified, ambiguous answer, but here is some questionable insight from my personal experience:
PyQt relates to cPython in a way that is very different than .Net relates to IronPython.
While IronPython is built on TOP of .Net, PyQt is a BINARY, semi-automatically generated set of bindings specific to a version of cPython against which it was compiled.
For a variety of reasons, i have problems running "standard" BINARY python modules against IronPython. Only the pure-Python modules that can be interpreted by IronPython as "Python" would ever work for me.
I am not saying "it can't be done," but I do expect you to have very bad experience with the set up if you manage to compile and install PyQt into IronPython.
Using PyQt from IronPython