I guess you could, but remember the cowl is structural, when you remove it the front "clip" will drop, with or without the engine. Without the cowl I can move the front frame up and down by hand. You have to make sure everything is straight again before welding it back in. It will certainly make it much harder having to reach over instead of being able to stand in the engine bay. Spending the time to pull the engine may well save you time in the end.
'65 A-code coupe, T-10 4-speed, 8" 3.25 limited slip