I think a good crux-question could be “Can one have faith in Christ and in works for receiving and/or retaining salvation?” I believe the answer lies within defining "faith in Christ."
Romans 10:9 could be the most applicable when addressing faith in Christ because the doctrines contained therein are universally related to all the Scriptural (not man's) articles of faith in Christ. I think it's also important to note that believing in Christ is synonymous with "receiving" Him, as in John 1:12; Rev 3:20.
"If you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved." "Confessing" or acknowledging the Lord is the same intention as in Matthew 10:32, 33, which also incurs "denying" Him. Not as Peter's verbal denial which was not truly in his heart, evidenced by his remorse and eventual lifestyle; but the absence of an outward lifestyle in accordance with Scripture, "as the Holy Ghost teaches" (1 Cor 2:13). This complies with Titus 1:6 and James 2:17, 18, 22, 24, and 26.
Can one accept these two articles as truth without being affected by believing in something untrue, which is not truly related to these articles?
I'm convinced that one can believe or disbelieve in any doctrine which is unrelated to faith in Christ (Rom 10:9 articles) without detracting credibility from their faith in Christ. It's through faith in Christ that saves (Eph 2:8); all else is only affects growth in the faith.
I believe John Gill's commentary presents a good explanation here: "That if thou shalt confess with thy mouth the Lord Jesus,.... That is, if a man shall make a good, sincere and hearty confession to God, before the church and people of God, and before the world, that Christ is his Lord and Savior, whom he desires to serve and to be saved by; and this as arising from a comfortable experience of the grace of God in his soul and from a true faith in Christ in his heart.
"And shall believe in thine heart, that God hath raised him from the dead, thou shalt be saved; for this article of Christ's resurrection includes the several other articles of faith: it supposes His death, and that supposes His life and the obedience of it; and His life implies His being here on earth and that His coming down from heaven to do the will of His Father; and this is the rather mentioned, which is here ascribed to God the Father, though not to the exclusion of the Son and Spirit, because that Christ is risen again for our justification, with which true faith is principally concerned.
"For such a faith is intended, not which lies in a mere assent to the truth of this, or any other article of the Christian religion; but which is concerned with Christ for righteousness, life, and glory; and with such a faith salvation is certainly and inseparably connected."