My question is, are we the "body of Christ" under in kind of covenant?
According to the Random House Webster's College Dictionary, a covenant is defined as follows:
covenant /kuv"euhneuhnt/
n.
1. an agreement, usu. formal, between two or more persons to do or not do something specified.
2. the conditional promises made to humanity by God, as revealed in Scripture.
3. a formal agreement of legal validity, esp. one under seal.
v.i.
4. to enter into a covenant.
v.t.
5. to promise by covenant; pledge.
6. to stipulate.
[1250-1300; < OF, n. use of prp. of covenir < L convenire to come together, agree; see CONVENE, -ANT]
While a lot could be said about number 2 above, I do not think that we are under any kind of covenant with God.
Any eye opening comments?

Great Question!! I would tend to agree with you, Earl.

I have heard Pastor Cole refer to the covenant of GRACE and while not wanting to speak FOR him, I think that what he refers to is the definition under #2 of your headings listed and I would go as far as to think that #3 applies as well. Grace is a formal agreement that we are saved by grace thru faith in the finished work of Christ, and the seal is the seal of the H.S.
The most important distinction to be made, as you well know, is that the OLD and NEW Covenant that is most commonly referred to has to do ONLY with the Nation of Israel. We see this clearly from Jer. 31:31. The dispensation of the GRACE of God is the program thru which God is graciously saving all of mankind today, without distinction.