No, you must be able to see to be able to see normally in darkness.
The blinded condition says:
A blinded creature can't see and automatically fails any ability check that requires sight.
If devil's sight granted conditional immunity to the blindness condition, it would say so. As written, Devil's Sight improves sight; if you are blind, there is no sight to improve.
In answering a similar question about truesight, nitsua60 writes:
The only thing Truesight does in this case is magnify the ability that was lost to blindness:
Truesight enhances one's ability to see: through magical darkness, invisibility, illusions, shapechanges, and into the Ethereal (PHB p.185).
But the blindness condition now says "you can't see. The sight through illusions, darkness, &c. which you so enjoyed just a moment ago, you don't have anymore (PHB p.290, paraphrased)."
In similar fashion, Devil's Sight only improves that sense which is lost entirely to blindness.