Succulent experts: can I get away with a pot with no holes?

Sure, just mist them often as was mentioned, rather than conventional watering...and use a soilless mix, but not one that is heavy on peat. Something like Schultz Cactus Potting mix should work great.
 
I have that same planter! Mine is just like your picture except mine has a little crack on the back. I think it's a Royal Copely but I've never been sure. I keep the planter on a windowsill and I have two pots with plants inside it. I pull out the pots to water and put them back in the planter once they've drained. You can't see the pots from across the room, only close up.

I have a very large collection of old figural planters and none of them have holes. I can't bring myself to drill and ruin their value so I find little plastic pots that fit inside. Sometimes I'll put a small wad of newspaper under the plastic pot to make sure the plant reaches the top of the planter.

I can tell you right now the plant on the far right can't handle much moisture. I let might dry out completely and then some before I water. The hen and chick plant also needs good drainage. I'm not sure on the other two but I really don't know of any succulants that like standing water.
 
I've grown succulents in pots w/out drainage holes for years. I have a few extras available if you're interested.
 
We finally sat down and planted these today... not in the original pot, but in a drained bonsai tray we had that was fairly deep and a nice size.

we used 3/4" of hydroton, a layer of wide open mesh, about 2 1/2" of succulent soil, and capped it with a mix of crushed red stone and red pumice around the center, with sand in the corners. I think it worked out pretty well. These photos are awful, but I wanted to post em up. I'll post pics with better light and angles soon.

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That's pretty sweet! Didn't realize the purple rosette one was so tall from the other pic.
 
Very nice! I have several of the ones you have. I will say the one on the bottom left seems to be a slow grower for me. However after it rained a lot outside, its growth picked up. Mine are outside in a very large pot that does have drainage and several hours a day of direct sunlight.
 
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