I don't run any WP with them so can't say what goes on in the gubbinssess when one does ..WP is arcana of the highest order IMO, but there are experts on it here.
Straight PHP forms and mailers on PHP pages not in WP , work fine with HG though, as do complex ones that I have that talk to / with outside XML streams at Y and Bing..
I don't use GA ( principle, they know enough already and I have other ways of getting reliable data that they don't see on sites that have no adsense on ;-)..Short of running a test of say 10 submits yourself and seeing what gets picked up or dropped or doesn't show..its hard to see what else you can do ..
I have always found them helpfull ..their phone support people do actually know tech and server stuff, and I wont host or reg with anyone I can't phone..24/7 if needed ..even if it means phoning transatlantic on my dime.
There'll be a WP expert along soon as they wake up ..they may bring a light with them ;-)