I have not tried it but I am confident it will work. I have a 100 amp hour lithium phosphate battery on my smaller boat for the trolling motor. Fully charged it puts out 14 volts. But car alternators put out 14V too. So the compressor can take it but I don't know if a steady diet of 14V will affect the compressor.
DC motor current draw decreases with RPM, which is why they have their highest armature torque at zero RPM. Many will recall that it was common practice to convert 6 volt tractors and vehicles to 12 volt, but no need to make changes to the starting motor. In fact, 6 volt starters (starting motors) last much longer when powered by 12 volt.
There is much confusion regarding motor loads because most people consider an electric motor to be a DC resistance load, ignoring the switching effect of brushes and commutator.
Many will also recall that a failing battery typically results in destroying the starting motor, because of the low voltage, low motor RPM = high current issue.
In my (70) years of starting systems & DC motor experience, I have no concern with operating my small compressors off 14 volts versus 12 volts, but great reluctance to operate them from lower voltage sources.
Another factor that is often ignored is the operating voltage question. A "12 volt" or "14 volt" battery is only providing that voltage at a low, or zero current (amps) flow. When powering a load, especially a significant load such as the compressor or starting motor, the battery voltage will be pulled down, often much lower.
The industry standard minimum voltage for 12 volt starting motors, applicable to other DC motors IMO, is 9.6 volts. If a "12 volt" DC motor is operating at a supply voltage below 9.6 volts, that is asking for trouble.
I would be grateful to learn how much the 100 amp LI battery voltage is pulled down by the load of your compressor. It the battery is capable of powering a trolling motor for extended periods, I expect it will be more than satisfactory for your compressor. A voltage measurement of battery voltage with compressor operating will tell the tale. By the way, batteries can be damaged by too high a current flow (draw) so I would be more concerned about battery damage than motor damage.