Powering the output side of a voltage regulator?
As a general rule, yes. It will damage the regulator. In some cases, regulators include protection to avoid this. This is generally found only in a few LDOs and should not be assumed unless the datasheet explicitly says so. This protection is in the form of a reverse biased diode, pointing from output to input.  When you power only the output, the diode conducts and sends it along to the input as well. Note that even in the presence of the diode, if you plan on doing it regularly and not just as an accident, additional care must be taken. Most LDOs with reverse diode protection specify maximum time and voltage that it can sustain. If you need more, make sure to include a decent power diode as well (the 4007 works for most cases)