You really need to get the exact specifications for the power input to those shocks to really tell. I'll tell you this though; your sled DOES make A/C power! You just need to tap into it BEFORE the rectifier (the rectifier is in the nose under the beer can holder).
Given that Fox makes shocks for MOTOR VEHICLES, I would *guess* that they are designing it to be compatible with the maximum number of vehicles. If you look at most sleds/bikes/etc. that do NOT have electric start, they have a 12VAC system with a variable frequency (based on the engine speed), using a voltage regulator to keep the voltage at or under 12V. It is with electric start that you begin to need a D/C power system, since that is what the BATTERY needs/provides.
If I were to further this guess, I would SUSPECT that this device would ALSO have a rectifier built in (a rectifier converts A/C to D/C), in which case you SHOULD be able to just plug right in to the D/C power system. This is because I see it as reasonably likely that the actual system is D/C, but designed for compatibility with A/C systems.
Again though, you really MUST confirm the power requirements with the manufacturer.
Also, do NOT plug in any kind of automotive-store inverter. These things (hopefully) convert to 120VAC 60Hz. You then would be running a transformer to convert to 12VAC 60Hz. How do you know that this device likes 60Hz?