What happens to my mail when I disable email routing?

I currently have email routing set up and enabled (and working fine). If at a later date I want to switch the email forwarding function to a different service provider, I must first disable email routing before I can change the MX records to direct mail delivery to the new provider’s servers. Because of the delay in propagating DNS changes, mail may continue to arrive at the Cloudflare servers for a while. What does Cloudflare do to the mail: queue, reject with a 4xx temporary error code, or reject with a 5xx permanent error mode?

Ideally, I would like to see the email routing decoupled from the DNS changes, so email routing continues to work until the rest of the world sees the new MX records and sends mail to the new service provider.