Thanks for the responses so far, but I've found my own solution. I did try a lot of different things, from writing a vbs script as suggested to a standalone program called hstart. hstart worked...but it creates a separate process which I didn't like very much because then I can't kill it in the normal way. But I found a simpler solution that required simply Haskell code.
My code from before was a simple call to runCommand, which did popup the window. An alternative function you can use is runProcess which has more options. From peeking at the ghc source code file runProcess.c, I found that the CREATE_NO_WINDOW flag is set when you supply redirects for all of STDIN, STOUT, and STDERR. So that's what you need to do, supply redirects for those. My test program looks like:
main = do
inH <- openFile "in" ReadMode
outH <- openFile "out" WriteMode
runProcess "rsync.bat"  Nothing Nothing (Just inH) (Just outH) (Just outH)
This worked! No command window again! A caveat is that you need an empty file for inH to read in as the STDIN eventhough in my situation it was not needed.