A clear NO

The Presiding Bishop and Prime Bishop Edward Pacaya:

differences and continued dialogue

It seems that the Philippines is the first Province to reject the Covenant. They do so from a firmly conservative perspective but they are not proposing to turn their back on the rest of the Communion. .

The reported grounds for rejection are ecclesiological - it's unAnglican.

The Bishops of the Episcopal Church in the Philippines have rejected the proposed Anglican Covenant, saying the proposal to centralise authority in London was an “un-Anglican” attempt to “lord it over” the Communion’s national provinces.
...
Bishop Malecdan stated the Philippine Council of Bishops “noted that the document provides for the creation of a Standing Committee that will be the ‘Supreme Court’ as it were, for the Anglican Communion to lord it over all Anglican Provinces. This, to the Council is very un-Anglican because of the autonomous nature of each Anglican Province. Hence, we are not in favour of the document.”

Their way forward is not to follow GAFCON into schism. Rather, as evidenced at the Dublin Primates' meeting:

We recognised that Anglicans have many disagreements as a Communion but we still can be agreeable to one another. We can still move towards reconciliation as sisters and brothers as a gift of God to us by persistently talking about our differences. This is the beauty of Anglicanism.

“Unity in diversity which is a recognized uniqueness of the Communion is preserved,” the prime bishop said.

The logic being that, if the GAFCON churches are to go their own way then there is no need for the Covenant. Therefore the remaining churches are grown up enough to persist in their differences. 

It also means that other provinces uncomfortable with the Covenant no longer need to equivocate by finding a form of words which seek to avoid them 'adopting' the Covenant. They can just say no.

Also at The Lead.