Do I need to glue 2x4 supports for an apron sink?
No. If anything you'd use construction adhesive, and not wood glue, but if you've done a good job with the screws glue isn't needed. In fact, it's rarely used in cases like this.
If you find that there's flex in your supports, re-screw it and make sure the boards are dead tight. Spread the screws widely in the vertical.