Thanks for the question.
The answer is no; Baptism is necessary for salvation.
Jesus made it a condition of salvation as He said, "unless a man be born of water and the Spirit he cannot enter the kingdom of Heaven," (John 3:5). There are other verses which support this such as Mark 16:16 and Acts 2:38. The idea of exceptions to the hard rule has always been of a certain amount of debate in the Church, but the consensus always was that certain classes of people, such as:
- the Saints of the Old Testament
- Catechumen (who were martyred while waiting for Baptism), and
- those who desired it (but were somehow prevented from receiving it)
These all received the grace of Baptism by God's Mercy. These alternative methods of Baptism were called Baptism of Desire, or Baptism by Blood (in the case of martyrdom).
So, we know that God can work around the strict limits of a rule, (He is God after all), but Baptism is the normative way. It can be dangerous to think that the exceptions outweigh the rules but, by the way people talk today, it would seem that everyone is going to Heaven (baptized or not) and few are going to Hell.
Any close reading of the Gospel will show that it is the other way around.
The hardest issue for us to fully explain, is for those that bear no personal responsibility for sin, i.e. the unborn — so we must trust them to God's Mercy.
In the past, the conventional view was that they go to limbo should they perish before Baptism. (A place of natural happiness which is neither Heaven, nor Hell), but that has never explicitly been codified into doctrine. There was still much to be hashed out.
- If Limbo were true as a permanent destination, for example, why is there no mention of it in Scripture?
- Would it be a temporary state? (whereas each soul would have to make a decision for or against the grace of God offered to it -— much like when Jesus "went to the spirits in prison," those who were disobedient in the days of Noah [cf. 1 Peter 3:18-20] esp. verse 19)
So, we must conclude we don't have all the answers completely clear in every case — that is God's purview, and in those unusual circumstances we must pray for God's Mercy.
What we can be clear on is the four (4) last things:
- Heaven and
To that end we must obey Christ in everything.