Is my plan to add a neutral wire to a switch box ok?
What you have -- ? 

Note that colors signify function, even though the actual cable color is whatever standard cable colors are.   Here, red is switched-hot, white is neutral.  



You can't cross the streams - er, send current going in a loop. This is AC.  It'll do bad things.  

A basic rule is that currents must be equal in each cable or conduit.  Think about an army of ants exploring a tree.  Anywhere on the tree, if you count the number of ants that went up a branch, the same number will come back down.  Currents are equal in tree topology - but branches can't touch.  If an ant goes up one branch and comes down another,  currents are not equal.  Hence, circuits must be a rigid "tree" topology and loops must be prevented.

You see in the first drawing where there's a "Great Wall" separating the two switches.  

So we do the following.  



See how neutral goes a bit farther, but this avoids sending current in one direction around the triangle, and it is a tree (vine, anyway) not a loop.  

**Notice how you will have two separate neutral splices in the left box.  Don't combine them and don't mix them up!