I'm afraid I have no idea who makes the decision. They can always "send a delegation," but I rather suspect Griswold or somebody else (at 815) has to supply, for example, an official list of delegates in order for them to be received as legitimate delegates when they arrive. Having no list is problematic, and I cannot imagine the offices at Lambeth trying to deal with lists arriving from every single diocese around the world. (I'm basing this guess on personal experience with an international committee where we operate by such rules; if you aren't on the list, you're an observer.)
If a list is required and none is sent, then those who go are just wasting time & money. Unless they're planning on demonstrating outside.
I'd have to go back to see exactly how the matter was worded, but I believe the communique asked ECUSA to not send a delegation, but instead to provide explanation for their actions. As I recall, the Primates' meeting doesn't have the power to actually deny ECUSA's attendance at the ACC.
So my guess is that it's Griswold's call, directly or indirectly, whether a delegation goes. Groups like the PEP (and they're not the first to talk about going regardless) will be pressuring him hard to send them; Williams will be pressuring him hard not to send them.
It won't sit well with the Global South if they go. Worse if they don't come with the requested explanation.
"So my guess is that it's Griswold's call, directly or indirectly, whether a delegation goes."
Griswold - The uninvited guest who crashes the party, overloads his plate with the best cold cuts, belches loudly, and wipes his mouth on the tablecloth. Every good host's nightmare.