I dont think it would. I welded the exhaust back on my F-150 with a stick welder and didnt fry the computer, so I think you would be OK.
As long as it doesnt become grounded it should be OK. If it doesnt electrocute YOU, I dont see it frying your computer. I worked as a heavy industrial welder build semi trailer 5th wheels and I would often rest my elbow on the workpiece to steady myself and I never once got shocked, so I think you should be OK.
Might be a good idea to just disconnect the battery though, better to be safe than sorry.

Cap'n