I would say probably not, the majority of the Kai would have some sort of sixth sense at one level or another, so the creature probably would not make it to the front gate alive.

But I would give it bonus points for sheer guts!

It probably is, but I guess it should be very hard. Such things have probably been done during the Helghast Wars. It wouldn't surprise me that the Brotherhood of the Crystal Star has put enchantments on the Kai Monastery to make such a possibility hard, but not impossible. That said, if you want a helghast to infiltrate the Monastery please do so.
As I recall in the core book it suggests that the Book of The Magnakai might have been stolen from the monastery by a Helgast specially bred for that very purpose. So if you want such a thing in you campaign there is a precedent.
hehehehe in lolw it was just two vassagonians that infiltrated, of course due to their shame in being beaten by vassans the slaves of kai cooked up some conspiracy theory involving helghasts