No, I don't think so. You can take a "normal" grip with the grip in the cup of your right hand and then rather easily get your right forearm on plane at address. It feels a little awkward at first but becomes second nature very quickly.
A normal conventional golf grip is where the trail hand is in the fingers of the grip as I understand it. I take it your quote around normal means not quite that. The SA grip goes through the palm of the trail hand with the grip end lining up with the forearm almost in the center of the palm ( the EIT). Are we talking about a grip somewhere between? I wish there was a posting by some of the hosts showing a picture of where the grip sets in the trail hand. Also is the grip in the left hand still a finger grip?