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A short answer to your question is yes, the connectivity check is done outside of the VPN. Check out this thread, which includes a (copied and pasted) response from the official GrapheneOS Twitter account: #1234
You can disable the connectivity check on GrapheneOS, something you cannot do on other OSes. You cannot force the connection to be done through a VPN as far as I know.
Also, you might want to read through this section of the website: https://grapheneos.org/faq#default-connections