No, I really don't think those who will be Raptured, have a real sense of it's coming. We may know it is growing close but certainly not the exact day or time.
Ephesians 4:11-14, are teaching the following:
Eph 4:11 And he gave some to be apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
Defines the various "offices" of the assembly, for the purpose of Corporate Worship and Edification. Which is defined in Verse 12.
Eph 4:12 for the perfecting of the saints, unto the work of ministering, unto the building up of the body of Christ:
Here we have the purpose of these offices explained. The "building up of the body of Christ", is in reference to Doctrinal knowledge and not to numbers of believers.
Eph 4:13 till we all attain unto the unity of the faith, and of the knowledge of the Son of God, unto a fullgrown man, unto the measure of the stature of the fulness of Christ:
The explanation continues in the above verse. The edification of the Saints, in Doctrine, brings about the unity of the Faith. No unity, in the assembly, can occur, apart from every member being likeminded, in regards to Doctrine. As our knowledge of Doctrine grows, we become "mature" in our knowledge. Each growing in stature, to be conformed more and more unto a likeness of Jesus Christ.
Eph 4:14 that we may be no longer children, tossed to and fro and carried about with every wind of doctrine, by the sleight of men, in craftiness, after the wiles of error;
The benefit of this "mature" Doctrinal knowledge is explained by verse 14. So that we will not be tossed TO and FRO by the Doctrines of man's imagination.
While this section of Scripture shows the importance of "sound" Doctrine, it does not lead one to understand the date and time of the Rapture. Just that there will be a Rapture, by virtue of proper doctrinal understanding of Scripture.
Additionally, I would like to add:
Many problems arise because of the differences in Eschatological thinking. The greatest of these, I believe, deal with the improper separation of the two purposes God has for Israel and the Assembly. Persons who disagree, that there are two distinct purposes here, usually do this on the basis, that it divides the "body of Christ". It does not.
Salvation, is all part of God's plan. He has executed it in several different ways but always by the same means. Example, there were those saved without Law, those saved under Law, those saved in the church age and those who will be saved, prior to the establishment of the Millennial Kingdom. Different ages or dispensations or economies, whichever is your favorite term. All those who are saved and will be saved, will be brought together as one Assembly, in Jesus Christ as it's head, at the end of the Millennial reign. For all things were made by Him and through Him and for Him.
However, there are distinctions, in the mean time, that must be observed. The wife of God, is not the same as the Bride of the Bridegroom. Israel, is not the church or vice versa. The Kingdom, is invisible right now, seen in operation within the Church but will be physical in the Millennial age. Christ is the invisible Head over the Church, the Great High-Priest but will be the visible King of kings over the physical Millennial Kingdom. I could go on but hopefully you see my point.
Therefore, the Church, will be kept from the hour of trial, that is coming upon the whole world. It will be Raptured as the Tribulation begins because the Lord will be revisiting Israel during the Tribulation. When the Tribulation begins and the Church has been Raptured, it will be as if the Church age has been removed from the timeline and the Tribulation is slammed up against the Nation of Israel and the world, to continue the Old Testament prophecies, right where they left off, before the first advent of Jesus Christ. Thus, God will fulfill all of the promises given to Israel.
John the Baptist or better, John the Baptizer, stood with one foot in the Old Testament economy and the other in the New, proclaiming the the Lamb of God in the New Testament. He was used by God to Transition from one economy to the other.
Peter and the other ten, (Excluding God's chosen traitor), were the first stones laid upon the foundation, of the church Christ was building. Jesus Christ, of course, being the Chief-Corner Stone. Thus, they were hearers, of both things, things intended for the Jews and Israel and things intended for the church. Having been raised in Judaism, it was difficult for them to except Paul's Ministry to the Gentiles. It was also difficult for them to get out from under the baggage of their religious upbringing. This is why, Peter and Paul did not always see eye to eye but the Holy Spirit brought about unity, in the end.
I'm saying a lot of complexed things here, gleamed from all the Scriptures, in a very short discourse. I hope I did not lose you.