I planted some green pepper seedlings in the past years, and more planted this year, too...they are so good and crisp when they are home-grown! The answer to your question...and from my own personal experience in growing green pepper plants is...yes...the peppers will turn red eventually! Color turning takes a bit more time, but have patience and your peppers will turn red. Guess that's why red peppers cost a little more at the market...they need extra time to develop that pigment.
Hope this helps!