Based on the following statement about spells then they should be able to Know a spell with Metamagic already applied to it.
"These new spells can be common spells chosen from the sorcerer/wizard spell list, or they can be unusual spells that the sorcerer has gained some understanding of through study."
If allowed by a GM, you can create a variant spell, like Empowered Burning Hands, maybe call it Cinder's Fan, but using up one of your known 3rd level spell slots. As a new spell, if approved, it wouldn't require you to possess the feat Empower spell, but a DM may exclude it from being further Empowered. Remember though, you are using one of your known spell slots which you can change out a single spell from every time you level up (one level lower than your max allowed spell level), not at every rest like prepared casters.
With Great Power comes Great Limitations!
Thank you this will allow what I am wanting to do.