Would this 5.5V transient voltage suppressor be damaged at 15V?
Would you consider it likely that this thing is broken/damaged?

Yes I would but, there are certain things you can decipher from the data sheet that might help you see why (such as this): -

So, with an ESD discharge voltage of +8 kV, the TVS diode would limit the peak voltage to about 12 volts. To get deeper you have to look at what MIL-STD-883 is all about. MIL-STD-883 is the human body model and uses this test circuit: -

So, 8 kV is the charged capacitor voltage and, due to the current limiting resistor (1500 Ω), only 12 volts is produced across the device when subject to the ESD surge. This means that there is an initial peak current of: -
$$\dfrac{8000-12}{1500} \text{ amps} = \text{5.32 amps}$$
So, if you applied a continuous 15 volts, there has to be more current flowing into the tiny device than 5.32 amps so, ask yourself, how long will a little tiny device last when having 15 volts across its terminals and a current of (maybe) 10 amps flowing. That's a power of 150 watts (or maybe it's 100 watts with a little bit of hand waving).
Or maybe your 15 volt supply was current limited to 2 amps but, again, how long would a little itsy-bitsy device in an SOT23-6 package last with maybe 15 or 20 watts applied?
My guess - a few milliseconds - how long was the 15 volt supply connected? If longer than a few milliseconds then this device has gone to meet its maker; it's an ex-TVS diode, it's passed-on; it's a stiff; it is bereft of (useful) life; it's shuffled off its mortal coil and joined the choir invisible.