Hi pjseaman,
It depends on the type of fluxcore wire you buy, whether you can run it without gas or not. Some FC wires are self-shielding and others aren't. What we use in our shop is dual shielded (ESAB 111-AC w/ 100%CO2). Many Steel Erectors will use the self-shielded wire because of the fact that a "slight" breeze won't disturb the shielding around the puddle, like with the dual shielded type.
I too have welded thicker materials with my little Hobart Handler 135. Many passes and lots of time to get the joint filled, but it made it. Like GRoberts stated, be patient! That machine wasn't designed for thick material and the duty cycle is really low. If you are routinely welding thicker materials, I would suggest investing in a machine that would handle it rather than torchering that little Lincoln repeatedly.
John Wright