Yes
Salvation is of the lord, and absolutely no part of it is dependent upon any conditions of doing good for God (Tit. 3:5, 2 Tim. 1:9). Being saved is completely up to God who has willed to save those whom he has given to his son Jesus Christ. Therefore the saved can never be lost (John 10:27-29, Rom. 8:35-39). Pretenders will fall away, but true believers in Christ persevere to the end (Heb. 6:1-12, 1 John 2:19).