Can I run singlespeed with the rear mech still in place, or has it got to come off?
It's a slot dropout inbred, so tensioning isn't a prob, but does the mech get in the way?
I've two rear wheel and would like to easily swap them round

I think you would be OK, whether you run the chain through it or not (presuming its not a seperate 1/8 chain).

I assume you would be ok as well but have never tried either.

why bother with singlespeed then, why not keep to one rear wheel?

if you have a single speed specific rear wheel then you may have problems as the rear mech may not have the same chain line as the rear cog. If it's a normal rear wheel with spacers+cog set up you may be ok. Why not just have a single speed and ditch all the weighty geary crud?

you may not get enough chain tension, you may be dropping the chain a bit.
chain size may be an issue as well since most sprockets run on 3/32 or 1/8???

I reckon you'll be fine – should be able to use shifters to pull the mech away from chainline ?

(to be honest, you might as well just stay in 1 gear using the mech since you're not losing any stuff off the bike, or am I missing something ?)

Your biggest problem will be with the chain skipping. I'm assuming you mean take out 9 speed wheel, replace it with wheel with 1 sprocket. Singlespeed sprockets get horribly hooked and a slipping chain on a singlespeed tends to result in a stem shaped hole in your knee.