Figure 1 - What voltage if I measure between +15 and -15 and what polarity?

Figure 2 - What voltage if I measure between +15 and -15 and what polarity?

 

30 volts in either case and polarity read will depend on on which line the meter probes are placed. Since you are measuring between two defined points the Ground symbol in the second image means nothing. It's a matter of point of reference for your metering device.

Ron

 

Is there a problem grounding the +15 on either schematic to obtain -30? Or would that even work?

 

If you ground either +15 or -15 in Figure 2, you are creating a short circuit. If the power supply is not short circuit protected then expect to see sparks fly.

 

Is there a problem grounding the +15 on either schematic to obtain -30?

In Fig 1 you can do that providing the supply is truly isolated and you don't ground the original 0 rail. Just treat the +15 as your 'new 0' and ignore the original 0.

 

Look at another example.
How would you create -18V from two 9V batteries?