Will a 1984 stock Chevy 350 take Vortec heads?

No, a 1984 stock Chevy 350 small-block will not directly accept Vortec heads without significant modification. Vortec heads (specifically the later generation ones like the 1996-and-later) have different bolt patterns, valve locations and possibly different lifter arrangements, making them incompatible with a pre-Vortec 350 block. You would need custom machine work, possibly including new valve guides, and potentially other modifications to make them fit. It's a much more involved project than a simple swap.