You will get about 15 hours on a fully charged battery which will bring it to 50% using just that device. The OEM battery is about 100 Amp Hours and it can be safely discharged to about 50% or maybe 30% without damage. Further discharge will reduce its capacity for future use.
If you plan to run the furnace, that is also 3.5 Amps to run the fan, but it doesn't run very much unless it gets real cold, so keep that in mind. You will have to charge the battery every day. The OEM converter doesn't do a very good job of this, so definitely, get it on charge. The generator will be running most of the day and you won't be able to see what is happening to the battery without further instrumentation. The light device by the sink is a rough indicator.
IMO, you should upgrade the 12V system for this critical need. I put in a PD9160 (60 amp) converter which can charge the battery in 30 to 60 minutes for the type operation you describe. I highly recommend that unit -- actually the PD9145 (45 Amp) is even more appropriate. In addition, you might be wise to put in a second battery.
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