Deep Cycle Batteries and Car Starting batteries are designed differently. A Starting battery is fully charged at 12.6 volts. A Deep Cycle Battery is fully charged at 14 volts.
A starting battery can have all the charge dumped in it very quickly since it will reach full charge before heat can build in the battery from the charging process.
A deep cycle can take a starting battery charge quickly, and then the charge needs to decrease as the battery slowly builds to 14 volts, or the heat will damage the battery or shorten its life if it doesn't cause the case to swell or the plates to short. It takes a minimum of 24 hours charging for a deep cycle battery to reach full charge, after being discharged.
So the simple answer is, yes your car starting battery charger will work, but it will only give your deep cycle battery 12.6 volts, enough electricity to start an engine, not enough to run a device for a prolonged time.