Somewhat, yes. The term is used, "when you are gathered together." I believe very strongly from personal experience, early church references, and the above scriptures themselves that there is a distinct power to be found in CORPORATE prayer which can be found no other way.
But Paul's presence not the same thing?
I've felt power in corporate prayer. Feelings aren't the same thing as Biblical doctrine. The feeling may indicate a more heightened trust in God. In fact, that's exactly what I think is happening. Those feelings can happen in other situations also, where the power of God also seems "tangible".
Binding and loosing, it's about application of Law and doctrine. There's a clear pattern through Scripture. But it's not as glamorous as taking power over the unseen forces in the air.
If we were binding and loosing according to our own desire, why then is not more accomplished? When then is it not more plainly taught? Why do we not see the practice of it in Scripture?
Examples given may look to one as a binding or loosing, but the words aren't used, and in other places, they are, but in reference to the application of Law and doctrine. Bound, you were on the hook to do it. Loosed, you were not.
@Mayflower
Romans 7:1-3 KJV
1) Know ye not, brethren, (for I speak to them that know the law,)
how that the law hath dominion over a man as long as he liveth?
2) For the woman which hath an husband
is bound by the law to her husband so long as he liveth; but if the husband be dead,
she is loosed from the law of her husband.
3) So then if, while her husband liveth, she be married to another man, she shall be called an adulteress: but if her husband be dead, she is free from that law; so that she is no adulteress, though she be married to another man.
This is binding and loosing.
"having been bound in heaven", God's assurance that they will be accurate. Or, power over the fallen angels, and the demons, and people. There are certainly different views on this.
Much love!