Engagement and baptism are two different things; baptism is to answer the call of divinity while engagement is the result of sensual desires of the flesh. Being Baptized has no relation in getting married or being engaged.
The bible made us to understand that even though we are engaged or married without being baptized, it doesn't matter but the only thing is that the engagement or marriage should not be a hindrance for us to be baptized. Baptism is recommended to believers once he or she have understood the teachings of Christ. Pastors who refused to wed a couple because the wife or the husband has not being baptized are going against the will of God because baptism do not have anything to do with engagement.
In as much as baptism and engagement has no relation, as believers, our marriage or engagement should not be a hindrance for us to be baptized. We should make sure we are baptized in other to answer the call of divinity.
God bless you all