It's likely the amp has enough power to damage the cab. Whether it will or not depends on how hard you push the amp and what sort of tone you use.
The reason I mention tone is because a cabs power rating is often based on the RMS power rating of the driver, rather than the designs actual mechanical power handling.
The RMS power is essentially how much power the voice coil can dissipate without burning out. The problem is the mechanical power handling below 100hz of many designs is actually less than the drivers RMS power rating. So, the 250W rating of your cab could possibly be a bit optimistic.
Mechanical power handling depends on both the driver's T/S characteristics and the design of the cabinet. So, if you put the same driver in two different cab designs, each design will have its own unique mechanical power handling characteristics.
Most bass cabs are ported designs. At higher frequencies ported designs behave essentially like sealed cabs. The port is tuned so that it starts to become resonant around the same frequency where the driver's response starts to roll off. The idea is the port will fill in and smoothly extend the output of the cab to a lower frequency.
Driver excursion tends to start increasing as the frequency drops below about 500hz. The excursion peaks just before the port starts to become active. As the frequency drops further, the port become increasingly resonant until Fb. Note. Fb is the port tuning frequency. As the port becomes more active it progressively suppresses cone excursion. So, at Fb the port is making most of the sound and driver excursion is largely suppressed.
Below Fb the output of the port drops of quickly and driver excursion increases drastically. Because of this, it's not a good idea operate a ported cab very far below Fb. The cab does not produce sound efficiently in the range, despite the fact that the driver is pumping back and forth like crazy.
Because of these factors, the excursion plot for the driver has sort of an S shape.
The following charts are the response plot and excursion plot for a medium ported design loaded with an Eminence 2512. The 2512 has a 250W RMS power rating, but this design is excursion limited to 175W, and it is recommended to run a steep HPF set to 40hz to protect the driver from over excursion below Fb.
View attachment 4622813
Notice the S shaped excursion trace.
Port resonance (FB) is at 55hz. Cone excursion is largely suppressed at FB, but notice how quickly excursion increase to Xmax below Fb. The trace turns from black to gray at Xmax, which equals 4.9mm. Also notice how fast the response is falling off in the top chart.
FYI the -3dB point (F3) for this design is about 73hz. The -10dB point (F10) is around 40hz. However the HPF is set to 40hz. FYI the HPF frequency is the point where the filters response is already down by -3dB. This means power sent to the cab is cut in half to 87.5W. So, with the HPF engaged, the system response will be down a total of -13dB at 40hz.
Hope this give you a little better understanding.