Years ago a mechanic friend of mine intentionally wanted to seize a Datsun engine by running it without oil (a long story). Took over 15 minutes, a lot longer than he expected. As a 16 yr old kid I inadverdently backed my Mom's '70 Mercury wagon off the ramps without oil while doing a lube job, probably about 20 seconds or so. No obvious harm at all. And through cumulative dry starts over an engine's life, it essentially runs many minutes without oil.
A deep cycle battery can provide a surge when needed, but nothing like the surge a car battery can. A deep cycle battery is also designed to be deeply discharged over and over again (something that would ruin a car battery very quickly). To accomplish this, a deep cycle battery uses thicker plates.
Choosing the right type of deep cycle battery charger will depend to a large extent on the design of your deep cycle battery. Determining the type of battery that you have can help in making the right choice a lot easier. Remember, one charger will not work for all types of batteries.