As said by @Marinebioacoustics it depends on your application.
If you only wanted to detect and count animals, then you can use SNR and sensitivity is removed. Only if you wanted to describe the sound characteristics then one would expect sound pressure values given in Pa.
In general, do not overvalue the purpose of calibration, because there is calibration and calibration.
A proper calibration of a hydrophones would give you sensitivity and frequency response for all frequencies of interest.
By definition the receiving sensitivity of a pressure sensitive hydrophone is given by the ratio of open-circuit voltage and free-field pressure. Both quantities are theoretical values: if you measure hydrophone voltage, it is not anymore open-circuit, and free-field pressure means that you need uniform sound speed without boundaries close by.
In short, there exist hardly reliable calibration data below 1 kHz as you need very large calibration tanks to remove surface and boundary reflections.
Also, I have seen sensitivity data of multiple identical hydrophones (ceramics only) and there are visible differences. The question now arises to which extent are the hydrophone different or how much contribute measurement errors. If you add preamplifiers, where capacitors are only specified to 5 or 10%, the amplitude and frequency response is easily modified.
Most hydrophone manufacturers give you a sensitivity that is valid within a frequency band limited by -3 or -6 dB. This means that your received level estimation could vary up to 3 or 6 dB. Sound propagation is such that depending on the distance you easily can have variations of a couple of dB, So it is hard to know if some variations are due to hydrophone or propagation.
A final observation: It is not only the hydrophone that counts, but also the whole system. Depending on the frequency, there may be resonances in the whole structure (recorder housing, glider, floats etc) that amplify or absorb incoming sound and must be considered or removed.