You can do lighting effects using the Lighting Effect Brush Load type. So with a low elevation setting you can get a nice shadow lip on a paint stroke so that it looks raised with a shadow from lighting on it. But it's going to be a part of the actual stroke itself as opposed to something physically offset like a drop shadow could be if you used layers.
You could do something with layers and ip ops or warps in Studio Artist similar to what you do in PS to do it as a post-processing step after drawing your interactive brush strokes.
This did get me thinking that if you could modulate things in the paint synthesizer based on the current index of 'repeat stroke' in path application that might open up some additional possibilities. You could then modulate a fixed offset path randomization based on that. So i'll look into adding that as a feature in the future.
Actually, you might be able to rig up something by using a custom image brush that essentially has 2 nibs built into it. Think of it as 2 offset circles you are drawing with. the bottom circle would be full back and the top circle would be a mid tone gray, then you would configure paint fill setup with a dark or black fill from and use the Mod Type in paint fill setup with an appropriate parameter setting to bring your actual paint color into the lighter top circle with the gray tone. So you'd essentially be drawing with 2 paint nibs, one for the drop shadow and the other for the actual paint color.
If you don't want the shadow to overdraw the paint color part of the stroke you'd need to work with the Depth Mask option in Paint Fill Apply.
I'll try to give this a shot if i get some spare time to build up the preset i'm talking about. Anybody else with some paint synthesizer editing experience feel free to jump in as well with your version of this kind of preset.
Another totally different approach would be to use interactive multi-pen with 2 nibs and then use the multipen nib modulator to darken the second offset nib. This is a different way to generate 2 offset nibs in a single brush you are painting with.
Here's an example using interactive multipen and 2 nibs. It's not quite what you want because the black shadow can overwrite the colored part of the stroke. But you could draw in such a way to avoid that happening.
Here's an example of a different approach. You'll have to wait for version 4 to use this particular preset but it does solve the black shadow overwrite issue with the preset above. This uses a normal interactive pen as opposed to an interctive multipen.