If a one-inch (or smaller in diameter) semp which has no visible roots is planted, how likely is it to survive?

If the semp has any stem still attached and the wound (cut/breakage end) is calloused (allowed to dry and form a callous) , then placing it on top of damp soil or planted in damp, but not wet soil, would increase the likelihood of rooting. When roots appear that should increase the survival rate of that semp.

Mark my experience is if you plant in bright but shaded spot for a few weeks this allows roots to form quicker. I keep my young newly planted offsets in part shade for 6 months

Very likely! Sometimes they will just sit there and wait for the weather to cool before really sending out roots (in my climate anyway).

You can also mist it enough that it dampens the surface of the soil/gravel. You just don't want to have it soaking wet. If you weather is hot and dry you can do the misting daily if the surface soil is dry.

There are three of them. Two with no roots whatsoever, the third might or might not have something, I am not sure. So far nothing croaked, they're just sitting there, as you described it. The one that's been there the longest popped out some time ago, I checked it - no roots. I put some stones around that one so that he stays put.

So far, the weather's been doing the watering for me - it's been raining every other day. To the point I'm actually worried they might have too much water, especially looking at a few others. But yes, I thought about misting them if it stopped raining. Good to know that's the right thing to do in such circumstances.

If they are in pot, move them out of rain temporarily until rain lets up. If in ground and getting soaked, put a vented cover over them to decrease amount of water they are sitting in. Hope your soil has drainage with addition of rock/sand/grit etc.

I agree with Bev, the amount of rain they are getting could be very hard on them since they have no roots, or very little roots.

No, there was no place left in the pot. They're in the ground. Along with all others, they are in a marginally elevated location, so they aren't sitting in a puddle even after heavy rains. As for rock, having read that their presence is considered beneficial, I've been gathering small stones from the garden and placing them among the semps, though so far they're mostly on or near the surface.

They say there will be 5 days without rain starting today... but they made similar claims before.

I would keep them in pots, away from full sun and rain. I did this last year and managed to save one of my semps. I also misted every week with half strength Quick Start. I always move a problem child into a pot and out of direct sun. There have been times my carport looked like a nursary. All new plants live there for a while too.