Depends on how much power the thing draws and how much battery you have as well as how much your TV's alternator puts out. Not a simple question with a yes or no answer.
A common battery type used in many RVs has about 40 amp hours of available power. If that's all you've got, the more efficient unit @wa8yxm mentions will flatten your battery in about 11 hours, or a little less, unless your engine is running and alternator is supplying that power.
((NOTE: I said AVAILABLE power. Use more than that of the battery total power, and you will indeed KILL the battery, as in damage it.))