No, we don't believe that they haven't been saved - or rather, we don't believe that they can't be saved. We believe in baptisms for the dead, which is an ordinance for the dead who didn't have the opportunity to baptized in this life. The person can choose whether or not to accept the baptism )I don't know who wouldn't, but agency is still important), and that will give them the opportunity to be 'saved' as you put it. 
 
Hope that helps!

Q: Does that mean Mormons believe that noone who has been baptized or born again of the Spirit between the time when Jesus died and the Priesthood was restored is not saved?  
 
A: Absolutely not, those who had those ordinances performed during the great apostasy and even after the restoration without the proper priesthood authority can receive salvation like everyone else.  
 
What it does mean is since it was not performed by the Proper Priesthood authority that it has no binding effect in heaven and holds to weight for eternal life. Now like the millions who died before the birth of Christ though those who had unofficial baptism and confirmations by men without the Priesthood Authority are not condemned.  
 
There act of devotion is noted and to be praised, they will have the opportunity to accept these ordinances performed by proxy done properly by the authority of the Priesthood in the Spirit World.  
 
When we are saved on judgement day they will be there as well to inherit salvation with all of us as well!  
 
Where in the New Testament dies Jesus tell us that not only must you be born again of the spirit and of water (John 3:5-7) but also that in order to be born again you must be baptized by someone who has been annointed with the Priesthood of Melchizedek? 
 
I think all 4 Gospels make the point very clear, all 4 gospels tell of Christ traveling 4 days by foot from Nazareth to the river Jordan to seek out John the Baptist (the only man authorized by God besides Christ to perform baptisms). If proper priesthood authority was not required to be baptized Christ could of had any one baptize him in Nazareth and save the long and difficult journey to John the Baptist.  
 
You are correct if you simply read the words and not ponder there meaning there is no verse that says Christ travel 4 days of long painful travel to be baptized by John because he held the Aaronic Priesthood and was authorized to baptize people.  
 
What other reason besides Priesthood Authority would explain this unusual and in your opinion unneeded pilgrimage to John in all 4 Gospels? 
 
 
 
P.S. As I alluded to previously, as a correction to your statement the Melchizedek Priesthood is not a requirement to baptize. Priests in the Aaronic Priesthood can baptize as well, confirmation and the Gift of the Holy Ghost though can only be conferred by the Melchizedek Priesthood. 
 
P.P.S Also I like to point out that since The Church of JESUS CHRIST of Latter-day Saints is a denomination of Christianity it cannot have differences with Christianity. Just like the other denominations like Catholicism, Protestantism, etc cannot have differences with Christianity only with the doctrines of the other denominations.  
 
I know some hypocrites make false statements that the Church of JESUS CHRIST of Latter-day Saints does not believe in Christ but as any person with a pulse and a IQ above room temperature can tell our belief in Christ is in our vary name.

Also another important correction, John the Baptist did no restore the Melchizedek Priesthood to the Earth. He restored the Aaronic Priesthood in preparation for the Apostles Peter, James, and John to restore the Melchizedek Priesthood.  
 
John the baptism would not have the proper authority to bestow the Melchizedek Priesthood as he was not ordained to this Priesthood in his lifetime. Peter, James, and John though as the ancient Presidency of the Church of Jesus Christ do hold the proper keys and authority to bestow the Melchizedek Priesthood.  
 
This allows every member of the Church who holds this Holy Priesthood to be able to directly track there Priesthood Authority directly to Jesus Christ the head of the Melchizedek Priesthood and the true Church.