"Could gatherings like the ones Paul refers to happen today?". Surely, the answer would have to be "Yes".
Another question could be: "How was it that such things seemed to just happen among those early Believers?" (And many other Believers since, no doubt.)
Again, the obvious answer would be: "... by the working of the Holy Spirit".
Again: "Why are the kind of gatherings that were for building up, comforting and exhorting the Corinthian Believers not experienced today?".
An immediate answer may be" "Because they are not expected or anticipated".
But could does Peter give an answer as to the kind of preaching what was preached then? He refers to:
"... those who have preached the good news to you by the Holy Spirit sent from heaven ...", 1 Peter 1'12.
In fact, he was the first to "preach the good news ... by the Holy Spirit sent from heaven" on the Day of Pentecost.
As well as him there's John, Philip and the others who went to Samaria, Aquila and Priscilla, Timothy and Paul.
He was more specific, saying:
"... my speech and my preaching were not with persuasive words of human wisdom, but in demonstration of the Spirit and of power," 1 Corinthians 2'4-5.
And what was the aim of his preaching?:
"that your faith should not be in the wisdom of men but in the power of God".
Further to that he explained:
"I will come to you shortly, if the Lord wills, and I will know, not the word of those who are puffed up, but the power. For the kingdom of God is not in word but in power," 1 Corinthians 4'19-20.
And "power" is the substance of the word of Christ:
"For I am not ashamed of the good news of Christ, for it is the power of God to salvation ...," Romans 1'16.
"For the word of God is living and powerful ...," Hebrews 4'12.
And Jesus, the Anointed One, the Lord, the word of God Himself is:
"... the power of God and the wisdom of God," 1 Corinthians 1'24.
The Greek word for "power" used here is dunamis and means "ability, power" according to Strong's Concordance. It is used 72 times in the Kingdom scriptures of Acts 2'1 to Revelation 3'22.
Should present-day Believers expect, even anticipate, this kind of preaching?
The Believers who took part in the very first New Covenant Kingdom prayer meeting obviously did. And the Holy Spirit affirmed them and made sure it was recorded.
They were direct and fervent as they asked for and expected to receive power:
"... grant to Your servants that with all boldness they may speak Your word,
by stretching out Your hand to heal,
and that signs and wonders may be done
through the name of Your holy Servant Jesus.
And when they had prayed, the place where they were assembled together was shaken; and they were all filled with the Holy Spirit, and they spoke the word of God with boldness," Acts 4'29-31.
We could challenge ourselves further and wonder if we simply don't believe as the early Believers did.
Is unbelief preventing Believers from receiving these powerful ministries of the Spirit? Unbelief is a very powerful thing. Look what happened when Jesus went "to His own country":
"Now He could do no mighty work there, except that He laid His hands on a few sick people and healed them.
And He marveled because of their unbelief. Then He went about the villages in a circuit, teaching," Mark 6'5-6.
Let us remember that "faith comes by hearing, and hearing by the word of God" Romans 10'17.
And added to that, let us heed these words:
"... earnestly desire the best gifts. And yet I show you a more excellent way".
"And now abide faith, hope, love, these three; but the greatest of these is love."
"Pursue love, and desire spiritual gifts, but especially that you may prophesy."
(1 Corinthians 12'31;13'13;14'1)