Let’s say I’ve already played 2 cards from my hand, and my opponent has an ember imp in play. Can I still use the ability from master plan to play the card I have stored under it?

Always helpful to quote the card text or link an image.

Ember Imp: Your opponent may not play more than 2 cards each turn

Masterplan: Play: Put a card from your hand face down beneath Masterplan.
Omni: Play the card beneath Masterplan. Sacrifice Masterplan.

If you have already played 2 cards, you may not utilize a card ability to play another card, as that would the third play.

Here are the cards in question:

Ember Imp

Master Plan

to add a side-note to this, the rules defines a clear difference between "Play" and "Put into Play", so had Master Plan said "Put into play the card beneath master plan" it could be done, which is annoying.