Yes, they will continue to believe, and over time, that belief will increase .... but that is not what saves - it was Christ's faith(fulness) to the Father that brings about our salvation. His faith is reckoned to certain people, through which, is their faith manifested unto them
Upon becoming born-again, the believer is given a renewed mind. Having a renewed mind, they would never, ever, consider or desire to return to un-belief. Why? Because in their heart of hearts and soul of souls, they know the truth. After all, are you able no matter how hard you might try, to make yourself believe something that you just truly don't believe? When saved, our understanding changes, with the old one never to return. Now, in the Bible we are told that there are those who do fall away, but they are never of those who were saved/born again: it wasn't a spiritual change.
So, to get to the essence of it all -- in all ways Christ alone is the Saviour and we are not.
[Rom 12:2 KJV]
2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what [is] that good, and acceptable, and perfect, will of God.
[Phl 2:12-13 KJV]
12 Wherefore, my beloved, as ye have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling.
13 For it is God which worketh in you both to will and to do of [his] good pleasure.
No problem regarding the timing of your response - do so whenever convenient for you. Have a safe trip.