Supply voltage of an op-amp
would this mean that a 17.5V is sufficient to produce a 12.5V output?

Most likely, yes.
But it's also important to check that if it's safe to apply 17.5V to the opamp. If the voltage swing is given for VCC=15V then the max value of VCC could be 15V (For example, LM324 and TL072 give the Voltage Swing values for max VCC). This should be checked from the datasheet.