Yes my pump is at the bottom... had to replace the wire once from a piss poor well Co that didnt install it right. Im sure you could get it wired out there to run it.... i would read the tag on the welder for the voltage. I have a plug in my garage that i use for the plasma cutter and i have a forced air heater plus use it to plug my gen in when the power goes out. You will just have to get the right plug. Im sure with the right wire you could do it.
i used 3- 8 SO cord spendy as hell
its not the volts its the amps the welder pulls.... that is what will cause the extension line to heat up.... the further the electricity has to travel the more the amps surge through the line.... it shouldn't cost anymore then $250 to have an electrician put a 220 outlet in your garage... depending on how far the panel box is in location to your outlet