I have a few road bikes, and it seems like the saddle position is dialed in reasonably well. I'd like to try the same saddle position on my touring bike, with a handlebar position that is higher and closer than on the road bikes.

Will this work, or do I need to adjust the saddle position with the different handlebar location?

On my 52cm '80s/'90s steel road bikes, the older MTB stems (prefer Specialized cold forged) work well to get the bar up to saddle height. They are not in the original style but look rather elegant and somehow safer to me. Guess I have fostered the imaginary terror of an emergency stop of some description resulting in my being impaled on a tall 7 stem.

Saddle position is independent of handlebars, generally speaking... saddle position should be where you are best balanced fore-to-aft and with the appropriate leg reach to the pedals.

It could change though, depending on how upright you go. If you are going from an aero position to a 45degree position (or from 45 degree to 90) then that might be enough of a change that you will want to get a wider saddle (sit bones will sit differently depending on your angle). Obviously, if you have to change the saddle, you'll need to readjust position a bit.

But for the most part, you should be treating saddle position and handlebar position independently if the bike is a good fit to begin with. Still, as you move more upright, you may find yourself sitting back farther on the saddle than you were previously, necessitating a move. I doubt it, but it's not out of the question either. Just listen to your body.

I'm not a fitter though, so take it with a grain of salt.

Two ways to do it:

If you have a bike with a threaded fork, a Nitto Technomic or Nitto Dirt Drop stem is the way to raise the bars.

If you have a bike with a threadless fork, you need a stem riser and either an adjustable stem or a short stem with 50-70 degree rise to raise the bars.

You might need a different (shape) saddle for your new, more upright posture on the bike.