Vault as Consul Connect CA when Vault uses Consul as storage backend

If I have a vault cluster using a consul cluster as storage backend, and want to use the vault as the Connect CA - is it ever possible? It seems they depend on each other.

  • Vault: needs Consul for storage
  • Consul: needs Vault for Consul Connect CA

Does Consul defer running consul connect until vault is up (e.g. retrying)?

Or should I use other vault storage backend (e.g. now integrated storage seems a good option)?