Will God forgive those who are not baptised if they ask him to?

There is a series of events recorded in Acts 10 that will help to answer this question.

In Acts 10 there is a man called Cornelius who, although he is described as ‘a devout man who feared God’ (v2), isn’t baptised. However, even though he isn’t baptised, God still hears his prayers:

About the ninth hour of the day [Cornelius] saw clearly in a vision an angel of God come in and say to him, “Cornelius.” And he stared at him in terror and said, “What is it, Lord?” And he said to him, “Your prayers and your alms have ascended as a memorial before God. [Acts 10:3-4]

…Cornelius said, “Four days ago, about this hour, I was praying in my house at the ninth hour, and behold, a man stood before me in bright clothing and said, ‘Cornelius, your prayer has been heard and your alms have been remembered before God. [Acts 10:30-31]

So, God does hear the prayers of people who are unbaptised (of course, it’s God’s prerogative if and how he responds to the prayers [and he will always do the right thing (Deut. 32:4)]).

When it comes to salvation and forgiveness, though, Cornelius still needed to be baptised. As it says at the end of the chapter:

…[Peter] commanded them to be baptized in the name of Jesus Christ. … [Acts 10:48]

So, God hears the prayers of people who aren’t baptised, but to receive salvation they still need to be baptised. As Peter said earlier in Acts:

… “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins…” [Acts 2:38]

Something further

It might be useful to ask, what was Cornelius praying about? As well as more “general” prayers, was Cornelius particularly praying for something specific? The next couple of verses (v32-33) might gives us a clue:¹

Acts 10:31-32
{31} …’Cornelius, your prayer has been heard and your alms have been remembered before God. {32} Send therefore to Joppa and ask for Simon who is called Peter. He is lodging in the house of Simon, a tanner, by the sea.’ {33} So I sent for you at once, and you have been kind enough to come. Now therefore we are all here in the presence of God to hear all that you have been commanded by the Lord.”

And now why do you wait? Rise and be baptized and wash away your sins, calling on his name. [Acts 22:16]

Notes
1. It also might be interesting to note that in Acts 10:31 it says that Cornelius’ prayer (singular) had been heard, which might also indicate that Cornelius was particularly praying for something specific.