It will void the warranty for you entire LCD system and if something goes wrong you're looking at minimum $1200 to replace the entire LCD unit.
I speak from experience. My LCD no longer flips when in potrait mode and the little hinge cover is lost. There is also some weird business where I have to toggle into a different mode to use my eye piece now.
Most people get by. But especially if other people ever use your camera it's not a great idea.
Get a flip unit adapter or an external mountable monitor.
Yes, it's a shame, the flip was so easy on the DVX. BUT, realistically, the already lousy quality LCD on the HVX becomes even more useless when using an adapter. Trying to judge what is sharp on the LCD is pointless, you need a real monitor anyway.