No, that gets you into purgatory. Yes, that eventually gets into heaven.
However, Heaven requires perfection.
I’m afraid of purgatory. Deathly afraid. Not as much as hell, but definitely afraid.
It is possible for one to proceed immediately to heaven upon death without purgatory. No doubt you have heard of the plenary indulgence, or a person dying immediately upon baptism, or baptism of desire or baptism of blood. In those cases there is no temporal punishment that remains. There is no limit to human perfection, so it is not achieved but a process.
Catechism
1 God, infinitely perfect and blessed in himself, in a plan of sheer goodness freely created man to make him share in his own blessed life. For this reason, at every time and in every place, God draws close to man. He calls man to seek him, to know him, to love him with all his strength. He calls together all men, scattered and divided by sin, into the unity of his family, the Church. To accomplish this, when the fullness of time had come, God sent his Son as Redeemer and Saviour. In his Son and through him, he invites men to become, in the Holy Spirit, his adopted children and thus heirs of his blessed life.
2028 “All Christians . . . are called to the fullness of Christian life and to the perfection of charity” (LG 40 § 2). “Christian perfection has but one limit, that of having none” (St. Gregory of Nyssa, De vita Mos.

G 44, 300D)
Baltimore Catechism
Q. 162. What is a perfection?
A. A perfection is any good quality a thing should have. A thing is perfect when it has all the good qualities it should have.
Q. 163. What is God?
A. God is a spirit infinitely perfect.
Q. 164. What do we mean when we say God is “infinitely perfect”?
A. When we say God is “infinitely perfect” we mean there is no limit or bounds to His perfection; for He possesses all good qualities in the highest possible degree and He alone is “infinitely perfect.”