If I'm playing as Pridestalker Legend and I play Kinkou Initiate when I have 4 Might out, will Rengar Legend proc Might to 5 before checking for draw?

Yes. Both abilities trigger simultaneously when you play Kinkou Initiate. You get to order them on the chain, so you can have the +1 Might land before the draw check.

Here's how it works:

• Pridestalker (Rengar Legend): "When you play a unit, give a unit +1 Might this turn."
• Kinkou Initiate: "When you play me, draw 1 if your other units have total Might 5 or more."

Both triggers fire at the same time. As their controller, you choose the order they're placed on the chain (Rule 333.1). Put Kinkou Initiate's ability on first, then Pridestalker's on top. Since the chain resolves Last-In-First-Out, Pridestalker's resolves first — bumping one of your other units to 5+ Might. Then Kinkou Initiate's ability resolves, checks your other units' total Might (now 5+), and you draw. This is confirmed by FAQ entries #9873, #10875, and #10585.