Welding and frames
I have have allways taken loose the batteries (2) in my vehicles to weld on the trail. This is because I use a ready welder that requires 24VDC to operate. I have forgotten to disconnect the battery several times when in the driveway welding with my MIG welder. Havn't had any issues with either computer or accessories fortunately! I would think that anything that could create a transient voltage spike could do damage even though current cpu designs are fairly well protected. Better to be safe than sorry in my book.
I would strongly caution you about welding anything directly to your frame though. Frame rails are formed and some are heat treated. If you weld a frame incorrectly or weld parts to it like rock rails, you run the potential of greatly reducing the frame strength. Believe it or not, drilling a couple of well placed holes for mounting hardly has an effect on frame strength (provided they aren't over the 3/8-1/2" diameter range). The subsequent bolted assembly can actually strengthen the frame assembly depending on the design. Think of it as a composite assembly, therefore stronger. Another nice thing about spending the time to make your rock rails removeable is that if they are damaged, you can easily remove and repair or replace. Or if you decide to change the design, much easier than putting more heat into your frame to change.
Sorry to ramble, my 2 cents anyway.