Yes to the first question; but I'm unclear as to what "regardless of the dispensation" means. In each dispensation, there is a certain plan of salvation that cannot be disregarded. I think Brother Chette was wise to refine your question somewhat:

No, certainly not. The people in the situation you describe were not responsible for knowledge of Jesus Christ, because He hadn't shown up yet. They were responsible for the revelation God had given them. For a Jew, it would be the Old Testament law; for some aborigine in Australia, or some Sioux Indian in North America, it would be the revelation of nature (Psalm 19) and conscience (Romans 1).

The revelation of nature is very, very specific. People could (and still can) learn all kinds of things about God from nature, which would be an excellent topic for a separate post (or thread). Anyway, God has always revealed Himself in one way or another, and people have been able to honor (or not honor) that revelation.

When Jesus came, however, the situation changed entirely. Even up to the time of the crucifixion, Jews were under the Law; and the Gentiles all over the world were following the revelations of nature and conscience. But once Jesus came, and was resurrected, the Gospel of 1 Corinthians 15 went into effect: faith in Jesus Christ, plus nothing!

The bottom line, however, is that, for most of human history before Christ, people were saved by a mixture of faith and works. And that's how it will be in the Tribulation. In the Millennium, with Jesus physically present, it'll be pure works: obey, or else. (I'm talking about survivors of the Tribulation, and people who are born during the Millennium. The Christians who returned with Christ from Heaven - - - us - - - will still be saved, because we've been saved since the day we trusted Christ.)

So, the obvious question is, what about people in our own day who have never heard of Christ?

I don't know. It certainly makes missions an important concern, doesn't it?

I suspect that such people (and, with worldwide communication, there are relatively few of them) are still under the nature/conscience thing, as in the days before Christ. But I can't give you Scripture for that.

The glaring exception is the contemporary Jew. Jews in our day, no matter how zealously they try to keep the Law, cannot be saved apart from faith in Christ.

Pardon the delay, brother; I stepped away from the computer for a couple of hours. And now I'm going to bed.