My question is when the verse says “But if you do not wake up, I will come like a thief …”, does it mean if they do wake up they will know the time?
I think you’re referring to Rev. 3:3
Remember, therefore, what you have received and heard; obey it, and repent. But if you do not wake up, I will come like a thief, and you will not know at what time I will come to you.
It’s a warning to the Church in Sardis to remember the sound doctrine they were first taught and obey it. I think this letter was written metaphorically to the main line church of today which has abandoned its Biblical roots, and therefore has no idea that the Lord is about to return, or what’s required of them to be ready.
Paul wrote that as believers we shouldn’t be taken by surprise when End Times events begin to take place, but should know that they are announcing the Lord’s impending return. It’s the people in darkness who will be surprised, and just when they think peace has come, destruction will come upon them suddenly and they won’t escape. (1 Thes. 5:3-4)
In Rev 3:4 the Lord said that there a few in these churches who have remained true to the gospel and they will walk with Him. I think He was saying that when the Rapture comes, some will be taken from the liberal denominations, indicating that there are some born again believers there.