The hood staying in place would be too restrictive and just another thing to get in the way. I think the engine hoist would foul up on the hood and then the engine coming up and out would hit the hood.
In my opinion, I would remove the hood, even if the whole radiator support panel was out too.

I wouldn't try it.  You're concerned about damaging the paint removing the hood, but I think there's a much greater chance the paint gets damaged trying to leave the hood on.  Listen to Rudi's recommendation.  Makes installation a snap.  Putting a couple layers of blue tape, and/or a little cardboard to prevent nicks and chips on the fenders, etc. is also a good way to keep things looking brand new. 

I did it on my '65 - easy peasy. I used one of the plates that bolts in place of the carb, and the hook from the hoist went directly to the plate - no chain. It's easier than everyone thinks it is.

https://youtu.be/qdHp1lFrnEk

I don’t want to talk about the summer I had my motor in and out 5 times, but I would pull it with the bell housing still on and after the first time I would leave the hood on as well. Much easier when doing by myself. Mine is a 68. I got to the point that all you had to do was break bolts loose and then just turn them out by hand, all threads were super clean. The key is either a intake plate or chain set up that was really close to the intake. Mine also has a 7qt oil pan.

I also pulled my engine in my 70 Mustang 4 times with the hood on this past fall and winter. There was a 1/4 inch clearance between the engine, radiator support and hood. I pulled the trans and bell housing first then turned the engine almost 90º after it was high enough. I had to go between the fender and radiator support because it arches up in the middle so it would clear the oil pan. I did it with a chain bolted to the heads twice and with a manifold / carb plate the other 2 times. It was the easiest when the engine lifted level. I left the hood on because I didn't have a place to store it. But you can mark it like these guys said. I used put masking tape on the hinges and on the hood around the hinges and mark where a line to line up when reinstalling it. It always worked very sucksesfulley to use 6S6's word.