Would he have forsaken them?

[Gurthang]

In one of the movies, I believe TTT, Sam questions why Frodo is being nice to Gollum. Frodo replies with:

Because I have to believe he can come back.

Now, it doesn't take a lot to deduce that he wants Gollum to be able to come back because that would give him hope. Yet this quote is very interesting, to me at least, because he specifically says that he has to believe. Why does he have to believe? It seems like he is almost saying he would give up without that hope.

If he knew that there was no hope for him to return to a normal life after the Ring was gone, would he have continued the Quest?