You are correct. There is no mention of scoffers. It is presumed that God told Noah that the flood would come in 120 years here:
Genesis 6:3 And the Lord said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.
It also says in 2 Peter:
2Pet. 2:5 and did not spare the ancient world, but preserved Noah, a preacher of righteousness, with seven others, when He brought a flood upon the world of the ungodly.
So it would seem that he did warn them.
I cannot find anything saying that anyone could have came aboard, if they wanted, either. Sorry for that assumption.
Still I have heard this parallel made but no scripture can solidify the concept..:
Just like then, preachers are warning people of God’s judgment for sin, the bad things we do when we know not to and the good things we fail to do when we know we should. And just as there was a Door on the Ark people could enter and be saved, there is a Door of Salvation today. That Door is Jesus Christ. Jesus is the only name under heaven and earth by which men must be saved. There was only one Door to the Ark; there is only one way to be saved from the judgment of our sin.