There will be a bit of time while a self-signed certificate will be on your site before Let's Encrypt gets verified. I'm not able to pinpoint how fast it was for me earlier this year when I switched from Comodo to Let's Encrypt, but it seemed to be a matter of hours.
It looks like if you try to switch to your Comodo certificate, I suspect the Let's Encrypt process will abort.
The good news is that once you get past this stage, the certificate renewal process is seamless.
p.s. I use Cloudflare, so it let me adjust my certificate settings while I transitioned from Comodo to self-signed to Let's Encrypt.