Not really as others have noted, the religious groups the left does have are either becoming more secular or remaining static. An increase for the religious left would have to involve defections from the GOP, and the Democratics show no indication of pursuing GOP voting traditionalists. In fact, they probably need them in the GOP tent to aid in their pursuit of prosperous suburbanites.
As TJ and Raphael noted, if anything, it's getting increasingly difficult for Evangelicals and practicing Catholics to identify with the Democratic party given their increasing emphasis on social liberalism. Barring Permanent Trumpism, I don't see any major movements.
Wouldn't the religious right have higher birthrates because of the whole no birth control thing or the be fruitful and multiply thing?
Well yes, but the difference isn't that large unless you're looking at relatively fringey groups; Quiverfull, trad Catholics, Ultraorthodox Jews etc.
