No. you either under the law or under Grace. if you sin while under Grace then you have the blood of Christ to cleanse you of your sin.
I see you are not the only one who is confused in respect to this. Romans 6:14 is very telling in respect to what it means to be under grace. One can start in chapter 5 and read on through to see the context as it comes to culmination in chapter 6.
Romans 2:13 is often mistranslated. It doesn't actually say under the Law it says in the Law. That being said in respect to those study it and it is the very thing that is their lifestyle. Hence why a lot of translations translate under. Galatians agrees with Romans 6. One can start in chapter 1 to find the premise and read on through as it builds.
Here are the ten verses where it is.
Rom 3:19 Now we know that what things soever the law saith, it saith to them who are under (in not under) the law: that every mouth may be stopped, and all the world may become guilty before God.
Rom 6:14 For sin shall not have dominion over you: for ye are not under the law, but under grace.
Rom 6:15 What then? shall we sin, because we are not under the law, but under grace? God forbid.
1Cor 9:20 And unto the Jews I became as a Jew, that I might gain the Jews; to them that are under the law, as under the law, that I might gain them that are under the law;
1Cor 9:21 To them that are without law, as without law, (being not without law to God, but under the law to Christ,) that I might gain them that are without law.
Gal 3:23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed.
Gal 4:4 But when the fulness of the time was come, God sent forth his Son, made of a woman, made under the law,
Gal 4:5 To redeem them that were under the law, that we might receive the adoption of sons.
Gal 4:21 Tell me, ye that desire to be under the law, do ye not hear the law?
Gal 5:18 But if ye be led of the Spirit, ye are not under the law.