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Quoting Paul with reference to the context is an exercise in schism. Paul contrasts Faith with the Law (works). As such his emphasis on faith is to counter the influence of the Mosaic influence of his listeners, particularly the Galatians. For anyone to read that and think the he means Faith alone, when he clearly means faith versus the Law of Moses is a great error. Justification is said to be without works in Gal.3:16, hence 'alone' I have to say again, that you and Luther are both adding the "alone." It is not Paul's meaning. How could it be when God himself emphasizes the works of the Good Samaritan, the charity of the Widow's Mite, etc. You are lost if you believe in Faith Alone.

Charity is the result of Faith (Gal.5:22-23)

Moreover, what Luther was saying was salvation did not come through a church, or a sacrament but by faith in the saving work of Christ.

Now, under any definition I would say that he meant alone without works, or merit (Eph.2:9)

If someone who is a Roman Catholic believes that he will be saved also.

if however, he is depending on anything else (baptism, communion) to be saved with, he is not saved.

This is no different for a Roman Catholic or a Protestant, who add works to be saved (baptism, join a church etc)