This question gets asked by all sorts of people: atheists, universalists (both the liberal and the supposedly-evangelical varieties), annihilationists. Anyone who opposes the justice of God eventually pops out this question as a final trump card. It really isn't so much.
Consider the Psalms.
In Psalm 19:1-4, David wrote:
"The heavens declare the glory of God,
and the sky above proclaims His handiwork.
Day to day pours out speech,
and night to night reveals knowledge.
There is no speech, nor are there words,
whose voice is not heard.
Their voice goes out through all the earth,
and their words to the end of the world."
In a poetic fashion, David here describes God's revelation of Himself in the creation. The inanimate creation doesn't use literal speech, obviously. However, the beauty, order, and balance of the universe tells us that it came from the hands of a God who provides both beauty and sustenance for His creatures. This is also described in Psalm 104:10-16, where various creatures are described looking to the hand of God to provide for their daily needs. Poetry, true, but does it not eloquently reveal that dumb animals have more spiritual sense that do most people?
An anonymous Psalmist made a similar point in Psalm 98:2: "The Lord has made known His salvation; He has revealed His righteousness in the sight of the nations." This time it isn't physical sustenance that is the topic, but rather the holy nature of God and the salvation that He has provided His people. That is, if dumb animals can depend on God for their daily bread, then men should know to look to Him, not just for bread, but for our spiritual welfare, too.
It is this latter revelation that the Apostle Paul describes in Romans 1:18: "The wrath of God is revealed from heaven against all ungodliness and
unrighteousness of men, who by their unrighteousness suppress the truth." But Paul looks at the other side of the equation. Where the Psalmists had described God's providential benefits to animals and to His people, Paul focuses on God's revelation of His wrath against unbelief. That is to say that there is no such thing as someone who has is ignorant of God, righteousness, and salvation or wrath. Rather, every man, woman, and child in the world has that information in every sensation coming to him from the world around him. However, the unbeliever hates that knowledge and suppresses it, puts it out of his consciousness, thinking thereby to avoid accountability for it.
So, in response to the question asked in the headline above, I ask a different question: should ignoring the truth exempt a person from accountability for that truth?