Hi Geo'!
If you have been running straight or arc'd handlebars, then your RST likely has a long top tube.
Yes, you will need a shorter stem and likely compact handlebars if you switch to drops. The reason why is because drop handlebars have hooks and brake levers that extend forward beyond the stem, and you need to subtract some of that extra distance to restore your former riding position. If you didn't compensate with a shorter stem and less handlebar reach, you'd be too stretched out to be very comfortable. Even so, it might not be workable, so you'll need to take some measurements first to see if the conversion will result in a comfortable riding position for you.
I would suggest first measuring the distance between your saddle nose and the center of your present handlebars to establish a baseline, then subtract the rearward distance where your hands actually rest on the grips (this allows for the slight bend in the handlebars, often ~5° of so). Keep that measurement in mind.
I just measured the compact handlebars on my Nomad and I get 120mm of forward extension measured between handlebar center and the "pocket" of the brake lever hoods where I rest my hands (with the levers set so the ends of the blades are even with the bottom of the handlebar). This is a pretty typical setup. Of course, the brake lever bodies can always be raised on the handlebars, shortening the effective distance to the hoods, but this makes them more difficult to reach from the drops.
If you take the measurement you noted above and subtract 120mm from your present stem, you can see what length stem you will need to put your hands in a similar place to achieve the same back angle on your RST with drops (assuming you ride in the most common position with your hands resting atop the brake hoods).
If your RST has a Long top tube, you will likely be stretched out more than you are now with straight/arc'd handlebars. By knowing the difference, you can see how much more you will need to reach.
Raising the handebars will decrease reach to a degree because the head tube is inclined rearward, so lifting the stem/handlebars will help. If your steerer is uncut, raising the stem is just a matter of swapping spacers. If the steerer has been cut, you might need a short stem that rises. I used such a stem when converting AndyBG's kindly loaned Raven Tour for my 2014 tour. I used that stem in a raised position. On my Nomad, I place it higher on the steerer, but declined so the clamp clears my steerer-mounted water bottles. The handlebars ended up in the same place on both bikes.
To accomplish the conversion, you will need that shorter and/or higher stem, compact handlebars, and either v-brake or cantilever-compatible brake levers, new brake cables, and new cable housing.
If you are running v-brakes, then you will need either Tektro RL520 Aero V brake levers or the equivalent model from Cane Creek, as v-brakes require a different cable pull ratio than road levers, and only Tektro currently make them (the Cane Creeks are rebranded Tektros).
The stem will likely need 50-60mm of forward reach. Despite claims to the contrary, I've found this provides sufficient reach for good control of my own loaded bike with drop handlebars. The key determinant is the distance (moment arm) between the brake hood where you have your hands and the center of the steerer. The change will affect the feel of the bike. Compared to a shorter top tube/longer stem combo, a shorter stem feels more like you are riding *in* the bike than *on* it, and more of your weight will be within the wheelbase of the bicycle -- again, compared to a similarly fitted bicycle with a short top tube and longer stem. For your conversion form straight to drop handlebars, the difference in overall feel should be less noticeable. Make sure the stem's clamp diameter matches the handlebars. The most common sizes are 25.4 and 26.0 and are not directly interchangeable, though a 25.4 stem can be shimmed up to fit a 26.0 handlebar clamp. Oversized stems and handlebar clamps are also available, but may result in a harsher ride.
You will need compact-reach drop handlebars. These are usually shorter in forward reach when measured across the top "ramps" between centerline and brake lever, and also have more shallow drops. If switching from straight handlebars (which are usually wider), I would suggest fitting fairly wide drops -- 44cm is good and will require less rider adaptation for width. Handlebars have all become wider in recent years. I commonly tour on bicycles with flared randonneur handlebars that measure 45cm at the ends but only 37cm between the brake hoods and have no problem when touring with a load. However, 44s or 42s will result in the least adjustment after your conversion.
Once you swap in the new cables and housings and tape the handlebars, you should be good to go mechanically, but be sure before dropping a penny to check your measurements. You may find your present bike is not a good candidate for conversion if it will result in you reaching too far even with a short stem and compact drops.
All the best,
Dan.