27. amps dc is 2.7 amps ac
2. 7 * 120 vac = 224 watts

1. gas generators are not mod sign wave only cheep inverters are. gas generators put out a true sign wave its just that there voltage can be off with load do to poor regulation and that can cause  problems with some smart chargers or if the voltage is really low your battery charger will not put out enough volts to charge the battery.
2. if you read the instructions that come with the generator it will usually say that you are not supposed to use both the 12v charging and the 120v outlets at the same time.
3. Kevin L's math is all goofy because your 120v battery charger is rated at 12 amps at 12v not 12A at 120v

those little colman suitcase generators with the briggs or tecumseh engines
have a flaw that you want to look into before you do any long term running under
a good load.

that is the epa compliant crankcase vent pipe is routed between the aircleaner and the carb intake.

what happens is when the aircleaner begins to clog the vacuum that is drawn will suck all the oil out of the engine, resulting in catastrophic failure, don't ask me how i know!

if it were me, i would disconnect that vent pipe and either vent it to the atmosphere, like the old non compliant engines or reroute it to the air intake side of the aircleaner so that there is no vacuum imparted on that line.

the advice to run it at 1200watts max is good advice as well, running at the peak output will likely shorten the lifespan of the unit.

i used one for some time on a service truck and i even turned the rpm down to 3000rpm for 50hz, it would still run my power tools and my lighting,, and the engine run's longer, quieter and with less gas as well.

i don't know how this might effect the charging rate at the 12volt plug, if it is regulated it might do just fine at the lower rpm albeit at a lower charge rate maybe.

suffice it to say, i am no fan of these little generators, but with a bit of attention and modification they can be pressed into service and get the job done in a pinch.

far better it would be to build a small engine driven alternator combo with a good regulator for charging your batteries, then you could set the engine speed to something more tolerable with the result being a better system in my opinion.

 If I were you, i'd run one or the other. I have studied the wiring schematics for my 5000w diesel, which has both DC output and AC output. It says expicitly in the manual, 'do not try to run a load on the DC circuit that exceeds its rated output- while running any-sort of load on the AC circuit. My genset will output 220 or 120vac, but only one or the other. With the DC its not recomended to use it at all, unless the AC is not being used. This makes sense to me, because Ive also pondered the use of 2 seperate DC inputs 'to a battery-bank under load'.

 In my mind, its better to leave the DC capabilite un-used, until you have to fall back on it, for emergency purposes.

 And why-not, most battery chargers(AC type) can output at least 50 amperes at 12volts.

 I got into this situation by an underpowered outboard alternator that only puts out 6amps @12v. Im running loads, my batt bank can carry them for so-long, yet volts will drop as im using these loads.

 Now take one of those 1000watt gas minigen-sets, I could plug in a 50amp 12v batt charger into that, then hook it to the batt-bank, but, I would be very sure, to disconnect the alt, from the outboard engine, before doing so. In that situation I could maintain battery bank voltage, without the DC output from the outboard.

 As long as I could maintain batt voltage under heavy loads, I really don't give a crap, about the DC output. In reality, im just offsetting the batt banks load with an AC source powering a dedicated charger. Since the AC side of the genset is flexing its muscle, its best not to stress it out, with the DC side running simulaniously.

But to answer your question- you would findout about any potential feed back thru the DC regulator the very first time doing such.