It is possible to do it without pulling the core support - you'll want to pull the oil pan off before and put it back on after. But, for as much extra trouble that you have to go through with clearing the core and the hood latch and trying to line up with the tranny mainshaft at that angle- even with the oil pan off - it is much easier to pull the core support. Been there, done that.

 

Pulling the core support is not that big of a deal. Pull the radiator first if you want to - it makes it a little lighter.