Disclaimer: I’m not going to pretend to be a wise theologian by any stretch of the imagination.
Well I won’t say your question is easy to answer, but I’m going to say that people who are sincerely searching for the Truth will eventually find God if they persevere and are open to His promptings. However, I wouldn’t use the Bible quote you refer to as justification for this belief necessarily. When Jesus is saying this to His disciples He’s speaking about believers who are asking for God’s help in prayer, not about non-believers who are searching for Truth/God.
However, if you read the beginnging of Saint Paul’s letter to the Romans, then you can make a solid Scriptural argument that those truly seeking God will find Him. Here’s the passage in particular that I’m thinking of:
“For the wrath of God is revealed from heaven against all ungodliness and wickedness of men who by their wickedness suppress the truth. For what can be known about God is plain to them, because God has shown it to them. Ever since the creation of the world his invisible nature, namely, his eternal power and deity, has been clearly perceived in the things that have been made. So they are without excuse; for although they knew God they did not honor him as God or give thanks to him, but they became futile in their thinking and their senseless minds were darkened. Claiming to be wise, they becam efools, and exchanged the glory of the immortal God for images resembling mortal man or birds or animals or reptiles.” - Romans 1:18-23
The Church teaches that one can come to know of God’s existence through the faculty of reason. I’m nearly positive there was a better statement to this effect made in the Catechism than this one, but this is the one I found:
286 Human intelligence is surely already capable of finding a response to the question of origins. The existence of God the Creator can be known with certainty through his works, by the light of human reason, even if this knowledge is often obscured and disfigured by error. This is why faith comes to confirm and enlighten reason in the correct understanding of this truth: "By faith we understand that the world was created by the word of God, so that what is seen was made out of things which do not appear.
Also, Saint Thomas Aquinas is known for his rational proofs of God’s existence, etc.
So I would argue that, with perhaps some rare exceptions (i.e. if you were living in an extremely remote part of the world and had never had any contact with Christianity whatsoever) you would eventually find God if you truly were openly seeking Truth. God wishes to have a relationship with all of us as we are all His children, so God would surely give everyone chances to know Him. But because God respects our free will, He would not force us into belief of course.