Of course. Even Judas was sorrowful over his sin, according to the Bible. The world is full of people who are disgusted at at least some of their sins, who seek to put particular sins behind them. This kind of sorrow is not how we have peace with God. While repentance is intimately connected to how and why God forgives us, it is not at all by itself a sufficient cause.
Properly speaking that repentance which “saves” is not merely a turning from, but is a turning to. We have peace with God because Jesus suffered the wrath of the Father that is due to us for our sin, and because He lived a perfect life. The work of Christ becomes ours when we, because of the work of the Holy Spirit in first regenerating us, repent and believe, or trust in the work of Christ. If we so trust all our sins are forgiven, because they have already been punished. This describes all our sins, past, present and future.
If our repentance includes turning to the finished work of Christ, if it includes trusting in His life and atoning death, the promise of God is that we will indeed be forgive (I John 1:9). Because His promises are true, we can and must trust them.