I raise this question because it has been floating around ever since the Reformation. Because we live in a country that has millions of both Protestants and Roman Catholics, it is worth asking.
However, there is a problem with the question itself. It assumes a simple yes-or-no answer for all Roman Catholics. The reality is that it isn't that simple.
My guess is that there are millions of Roman Catholics in this country who know Jesus Christ as Lord. There are also millions who do not.
I'm also guessing that there are millions of Baptists, Presbyterians, Methodists, etc. who love Jesus. I'm certain there are many who do not. Even within the non-denominational crowd both exist.
We do well to avoid lumping Christian groups together as a whole. We do much better to ask the question of one person at a time. A better question is, "Is that particular Roman Catholic saved?"
Of course, the only way to truly know the answer to the question is to get to know that Roman Catholic. When we spend time with people we can usually tell whether or not they know Jesus (God is the final arbiter in this, but we can usually make a pretty good guess).
A funny thing has happened to me along the way in life. My Protestant background suggests strongly that Roman Catholics do not know God because they are simply trying to work their way to heaven. However, when I have gotten to know a number of Roman Catholics, I've found that many have a deep love for Christ. They may use some different terminology than I do and have differing practices, but their commitment to Christ seems genuine.
It is easy for us to fall into the trap of holding onto a straw man argument when thinking of Roman Catholic theology. It is not a monolith. Beliefs vary. All do not agree with the Pope on everything.
Let's get to know people personally and talk about the things of God. When we do this, we gain a much better understanding of whether or not they know him. This gives us a real answer to the above question, one person at a time. This is much more accurate and valid than making judgment calls about entire groups of people.