I think that leaving the batteries connected or any of the wiring connected is in the category of "hard to defend if it screws up". There is so much current available from a welder and so little control over where it goes, that I would be tempted to disconnect the grounding wire from the trim tab before welding. What if all that current wants to go thru the wire to get back to the ground clamp? I assume that you have two ground leads so that you can clamp both hull and tab, or that you clamp the two pieces together during welding so that one clamp will do.
By the way, I can't weld. I am a NASA-certified welding inspector, so I don't need to, I just criticise. It's a great job.... :-)
I am planning to take a welding course this summer at the local community college if the dates work out. So I'll be able to criticise myself.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida