That is an excellent GTAW question.

I say it will not affect the equipment because the voltage rise occurs locally at the electrode/collet/collet body, arc stream (plasma) and the workpiece.

Apply a volt meter (of an appropriate rating) at the equipments output terminals with and without helium. See if you notice a change. I'm gonna try it next time I go down to my garage.

Hope you get more hits on this one.

Are you using the helium with ACHF or switching to DC with straight polarity? I also have a Lincoln SquareWave 175 and on occasion use 100% helium when welding thicker aluminum. The machine will indeed provide enough amp output to weld thicker aluminum but be alert to the air cooled torch and the amperage rating of this torch. Mine is rated at 125 amps (LA-9). There is also an optional torch LA-17 rated at 150 amps and LA-26 rated at 200 amps. I use DC and helium on any aluminum thicker than 1/4 inch when using this machine. Try DC and helium on thick aluminum. Once you get used to the puddle, I think you will expand your versatility with this machine.

Helium with its higher ionization potential (Vs Argon) results in more difficult arc initiation and operation at higher arc voltage. The higher arc voltage results in a higher heat input for a given arc length and current. There is a formula that explains this (to egg heads) but I think the meat of your question lies in the need to know if you're going to blow up your machine.

Your Miller will blow breakers when it draws too much current from an inadequate panel or exceeds its duty cycle; your increased arc voltage due to the switch to helium should not have a discernable affect on either.

As mentioned above Polarity can make a big difference in welding heavy sections. DCEN with helium can do wonders but must have excellent surface prep and conditions to be effective and sometimes a dirty casting simply will not allow itself to be welded with DC. Often times a mixture of helium and argon can offer an excellent compromise in AC operations where a little boost in heat will make a project possible that would otherwise become scrap.

Take to heart the above advice conserning torches and consider a water cooled torch if your going to be doing alot of high power work. Also a full length tungsten (where practical) will allow you to squeeze a few extra amps into your work.