I say no, I don't think so, because the gospel of salvation is not found in Peter or James.
Was not the "gospel" of which Peter speaks of in the following passage the same gospel which declares thatbelievers are redeemed by the blood of the Lord Jesus?:
"Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; 19. But with the precious blood of Christ, as of a lamb without blemish and without spot...Being born again, not of corruptible seed, but of incorruptible, by the word of God...And this is the word which by the gospel is preached unto you" (1 Pet.1:18-19,23-25).
Are not Peter's words "this is the word which by the gospel is preached unto you" referring to the gospel that these believers were redeemed by the blood of the Lamb?