I think so. since you have control over how much solder is in the initial puddle, you can use as much as you normally would. this puts the header a little farther away from the board, but you would presumably be doing this with all the other headers as well.
They'll be cold solder joints for sure, and it will be very hard to get enough solder on the ring to make a mechanically strong joint especially since you don't want the hole filled.
And how will you get heat transfer from the pin to the solder on the ring? Once you've got a few rings making the mechanical connection, you won't even know for sure if the others actually melted.
Though I haven't actually tried soldering it this way.
Maybe I should try not having it completely flush and see if I can get in with a fine iron tip.