C4's onward draw juice 24/7, but decent battery, clean connections (use very small dash of lanolin spray) and battery should last 6-8 weeks without issues.
Your radio and clock would only draw milliamps, most batteries have say 100 amp-hour, so drawing say 50/1000Amps or 50milliAmp it will take a long time to use up the battery. If you get some clear light a charger working off a solar cell may put enough back in to see it right for 6 months.
Of course there is no substitute for start & run up to temp at least every two weeks, better still come on a club run.