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Also, unless the monitor works on 14.4V DC - which it won't
I presume the OP is talking about a pro video monitor, which most often use a 14.8V battery standard derived from Sony camcorder batteries (or sometimes pro camera batteries directly).
There's a thing called D-tap for powering extra equipment off the same battery, although I'm not entirely sure how/if it allows daisy chaining.
grams
Brommers
CYOA
Almost certainly not. Not for long, anyway. Totally discharging a battery is a pretty surefire way to kill it, generally. I think you'll need a bit more capacity if you want it to work more than once for that length of time.
Also, unless the monitor works on 14.4V DC - which it won't - you'll need an inverter. Which won't be 100% efficient, because nothing is.