Good works will not get you into heaven. We are saved by faith in Jesus Christ not by good works.
Also, if you don't belong to the Christian faith, but also live in such a way that it is, keyword "comparable" to that of someone whodoes practice Christianity, then you are also going to Heaven, or your religion's version of it.
The answer is no if the one practicing a comparable life to Christianity and has heard the gospel and rejected it. In Romans Paul is addressing those who have never had the opportunity to learn about the Lord but who instinctly obey God's law.
The Lord has said, do not put your faith and trust in man.
This is correct, we are to put our faith in Him. Cults put their faith in doctrines and those who started the cult; other religions put their faith in their god(s). Paul addresses putting your faith in men in 1 Corinthians 1:
1 Corinthians 1:10-17
10 Now I exhort you, brethren, by the name of our Lord Jesus Christ, that you all agree, and there be no divisions among you, but you be made complete in the same mind and in the same judgment. 11 For I have been informed concerning you, my brethren, by Chloe's people, that there are quarrels among you. 12 Now I mean this, that each one of you is saying, "I am of Paul," and "I of Apollos," and "I of Cephas," and "I of Christ." 13 Has Christ been divided? Paul was not crucified for you, was he? Or were you baptized in the name of Paul? 14 I thank God that I baptized none of you except Crispus and Gaius, 15 that no man should say you were baptized in my name. 16 Now I did baptize also the household of Stephanas; beyond that, I do not know whether I baptized any other. 17 For Christ did not send me to baptize, but to preach the gospel, not in cleverness of speech, that the cross of Christ should not be made void. NAS
Men do not bring other men to faith in Christ or again as Paul wrote:
1 Corinthians 3:1-9
3:1 And I, brethren, could not speak to you as to spiritual men, but as to men of flesh, as to babes in Christ. 2 I gave you milk to drink, not solid food; for you were not yet able to receive it. Indeed, even now you are not yet able, 3 for you are still fleshly. For since there is jealousy and strife among you, are you not fleshly, and are you not walking like mere men? 4 For when one says, "I am of Paul," and another, "I am of Apollos," are you not mere men? 5 What then is Apollos? And what is Paul? Servants through whom you believed, even as the Lord gave opportunity to each one. 6 I planted, Apollos watered, but God was causing the growth. 7 So then neither the one who plants nor the one who waters is anything, but God who causes the growth. 8 Now he who plants and he who waters are one; but each will receive his own reward according to his own labor. 9 For we are God's fellow workers; you are God's field, God's building. NAS