A competent glass shop should know what they're doing, but make sure you explain what's going on, and make sure they properly clean up any rust/corrosion when they remove the old windshield, and take extra care to properly seal it, especially at the driver side.
That said, I think the bigger issue is a failure of the factory urethane sealant, not just that specific area (honestly, if it hadn't been shorting out the GEM, I never would have noticed it leaking in that area, because it wasn't a large amount of water that pooled or anything) - a few months prior to my leak/short issue occuring, I started noticing drops of water coming into the cabin at the passenger side top of windshield, when taking mine through a car wash, indicating (at least to me) that the whole factory seal job was failing.