Welding Advise Needed - Can this welder cope?

[magicniner]

It might just manage but you'd definitely manage that with a fairly cheap Machine 190A Mart MMA (Stick) welding set and get better results than gassless mig. Gassless mig was designed to deal with thinner sections than are not generally manageable with Stick without using shield gas.
Stick is a also great addition to your range of capabilities and I took the opportunity to add one to my workshop when a job came up that MIG wasn't suited to, don't forget that Stick works outside when it's windy and raining, can be used to weld Stainless (with the right rods) and you can also run a Carbon Arc Torch (Demonstration of The Carbon Arc Torch - YouTube ) with a Stick set ;-)