An awakened mythic is, on average, 2000 gems (500 gems per copy). Free players get about 667 gems a month (1/3 from completing all content, 2/3 from fortune shrine - if you have 500+ gems hoarded).
So, in theory, free players get enough gems to awaken a mythic every 3 months. However, that’s putting gems into literally just eggs that feature that one mythic so you’re giving up the opportunity to expand your collection of legendaries for that time.
Honestly, I wouldn’t even consider awakening mythics for the first year of playing the game unless you plan to spend lots of money. You’re better off getting lots of legendaries rather than a few individual mythics. I recently wrote an egg hatching guide which might be helpful to read: KD's Egg Hatching Guide