You may have seen it in a search, but here's my TI on the Harken Hoist.http://www.hobiecat.com/forums/viewtopic.php?f=73&t=23018
It's lived there, other than when it's out, since April 2010, and I have noticed no ill affects. I didn't use the straps, but built a narrow wood platform, to keep the amas, sail, etc, next to the boat. With straps, the extra stuff on the hoist would kind of pull up around the boat. I would definitely store it upside down. If you wrap the straps around the bottom, you would definitely notice some hull deformation.
I will note that about a month ago I got the Harken Hoister replaced under warranty. Luckily it's a lifetime warranty. One of the wheels in the tackle or traveler (whatever it's called) was breaking all up. I believe it had been doing this for quite some time, as when I installed the new one, the effort to hoist was a lot easier than I had remembered in the past. I didn't notice it until I saw plastic pieces popping out every time I hoisted. That and it became nearly impossible to hoist.