Yes,but I recommend grinding the zinc off wherever you want weld. Never tried it w/ flux core,but it can be a bear welding w/ stick.Maybe you already know this,but drink a pint of milk after inhaling that zinc smoke.Gets rid of the "zinc hangover" real quick.
Mike

You might want to look at a Thermal Arc Dragster 85. This is a very compact and portable inverter that runs off 110V.

It is a stick welder which is good for less than ideal conditions like zinc coating, rust, dirt, paint, etc. You could use 3/32" electrodes with it which will put down a decent bead and use multiple passes when necessary for bigger jobs.

A stick welder takes a bit more skill than a wire feed but I'm told that most 110V wire feeds are a waste of time.

The Lincoln flux core IS the way to go. If you ever need a higher amperage, borrow or buy a Lincoln "buzz box" stick welder. I'm on 10 acres and have the same needs for a welder that you mentioned.