Is there a way to tell the grit coarseness of an unmarked sharpening stone?
With some experience you can tell by running a finger over the surface. 

As a general guide:


grinding stones used for serious repair of knives form damage of long ngelect; will feel disticly rough, not as rough as sand paper but you can definitely feel an abrasive surface. 
sharpening stones : these will have a smooth surface but will have a definite 'drag' or friction to them, a bit like rough paper. These are used for normal sharpening of knives. 
Polishing/finishing stones : these will feel very smooth with just a hint of texture, a bit like magazine pages. Used for refinement and polishing of a cutting edge .