can purple mel activate empower without a target enemy unit

Yes, you can activate the Empower ability on Mel, Newly Awakened without a target enemy unit.

According to Rule 827.1.c.1 and Rule 827.1.b.1, the Empower keyword is an activated ability that specifically targets or requires no units to be on the board. The cost to activate Mel's Empower ability is simply [3], and the effect of that ability is only to make Mel "Empowered."

The text on Mel that references giving units -[M] is an Empowered ability (Rule 828.1.b), which is a separate, dependent effect that only becomes active after Mel has already become Empowered. Activating the Empower keyword does not require any targets; it only requires that Mel is not already Empowered.