This is going to be a wall of text. Apologies.
There are multiple experiences, states, and places which some Christians have mistakenly conflated together under the name "hell." The answer then is yes, but it's not unqualified.
Since we're discussing this in terms of universalism, I'd like to start with the fire and judgment of 1 Corinthians 3:10-15. Even those who are saved may undergo purgation and escape only as if through flames. Universalists understand that fire has a purpose - it is a test, a correction, a stripping away of that which is unworthy. We find this principle elsewhere:
Endure hardship as discipline; God is treating you as his children. For what children are not disciplined by their father? If you are not disciplined—and everyone undergoes discipline—then you are not legitimate, not true sons and daughters at all. Moreover, we have all had human fathers who disciplined us and we respected them for it. How much more should we submit to the Father of spirits and live! They disciplined us for a little while as they thought best; but God disciplines us for our good, in order that we may share in his holiness. No discipline seems pleasant at the time, but painful. Later on, however, it produces a harvest of righteousness and peace for those who have been trained by it.
Discipline means that God is treating you as his child. Is this the sort of unpleasantness which is associated with hell?
Let's take the more problematic words in Matthew 25: the unrighteous will be sent into eternal punishment. Sounds pretty conclusive. The root of the word here translated as "eternal" is
aion. In Matthew 13:39-40 and 49, though, Jesus refers to the
end of an aion, so it's not entirely clear to a universalist that this is eternal. Ages, another common translation, have ends. With Jesus, one
just ended.
In any case, I'm looking at this passage because of "punishment." The word and its associated verb, as far as I can tell, are only used four times in scripture. Here, of course. In 1 John 4:18 it refers to the fear of punishment, saying that the one who fears is not perfected in love. In Acts 4, it refers to legal punishment. Its use in 2 Peter is fascinating:
But false prophets also arose among the people, just as there will also be false teachers among you, who will secretly introduce destructive heresies, even denying the Master who bought them, bringing swift destruction upon themselves. Many will follow their sensuality, and because of them the way of the truth will be maligned; and in their greed they will exploit you with false words; their judgment from long ago is not idle, and their destruction is not asleep. For if God did not spare angels when they sinned, but cast them into hell and committed them to pits of darkness, reserved for judgment; 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 ; and if He condemned the cities of Sodom and Gomorrah to destruction by reducing them to ashes, having made them an example to those who would live ungodly lives thereafter ; and if He rescued righteous Lot, oppressed by the sensual conduct of unprincipled men (for by what he saw and heard that righteous man, while living among them, felt his righteous soul tormented day after day by their lawless deeds ), then the Lord knows how to rescue the godly from temptation, and to keep the unrighteous under punishment for the day of judgment, and especially those who indulge the flesh in its corrupt desires and despise authority.
They are
already in hell, kept under punishment by God, but this is their state until the day of judgment. The word Jesus used in Matthew is the current state of some people right now, who have yet to experience the day of judgment. Is this word used elsewhere in Greek? LSJ has some interesting entries:
It can even be used to refer to the disciplining of an athlete. So is this conscious torture? Read in context, it seems again like the purposeful chastening of a God trying to keep his children in line, sometimes in spite of themselves. Sometimes, very painfully.
What happens if a person does not accept Jesus? As it says in John 3:36, the wrath of God abides on him. Forever, right? John uses the verb for abiding 33 times in his gospel. In John 2:12, Jesus stayed for 3 days. He stayed with the Samaritans for 2 days. In John 9:41, when he says their sin remains, does he mean that it remains forever? No, he means it remains
until they repent. There is no indication here that this wrath of God abides forever. In fact, as the word is often used, we could understand this to mean that the wrath of God is abiding until the previous clause is fulfilled.
Is there hell? Yes. Salvation means one can enter into heaven. It does not mean it will be a pleasant process. Fortunately:
For his anger lasts only a moment,
but his favor lasts a lifetime;
weeping may stay for the night,
but rejoicing comes in the morning.
This is not a full case from the universalist perspective, of course, but this is already long enough.