No!
Revelation 20:4
“And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years."
A way of thinking can be changed, but not a permanent mark.
This will require an irreversible decision, not a compromise nor vacillation from which one can have a change of heart.
I always check the Greek before reading too much into the English tenses. Creating another category of unforgivable sins does not seem to be in the biblical intent here.
Revelation 20:4 is identifying those who were BEHEADED and martyred for witnessing and testifying of Christ Jesus who did not worship this beast and DID NOT accept the mark that the Beast requires all, both small and great to accept in the way they think and act (forehead and right hand).
It says nothing about a permanent mark there or in any verse in Revelation about this mark. This mark causes all who receive it to be deceived by the Beast - it says nor implies that the small and great receiving this mark are 'permanently marked'. Scripture tells us that the Beast and the False Prophet are thrown into the Lake of fire. It does not say all those with the mark and thrown in with them.
This mark is not permanent. Blasphemy of the Holy Spirit is the only sin that can never be forgiven. The reason for this is because when one hardens their mind and heart to God - it is impossible for that person to accept grace and redemption, and rejects God completely for his own belief system.
Of their own free will they reject Him, and they will wail and gnash their teeth against the Most High rather than repent and accept Jesus as their Lord and Master.