I've tried setting up multiple SSL-Certificates (using letsencrypt) for dovecot on my ubuntu machine. Used dovecot version is 2.2.18.

Regarding to official docs this should be working.

My test-client (Thunderbird on linux) has been mentioned to be working fine with SNI here:
https://wiki.dovecot.org/SSL/SNIClientSupport

https://wiki.dovecot.org/SSL/DovecotConfiguration#line-89

local_name imap.example.org {
  ssl_cert = </etc/ssl/certs/imap.example.org.crt
  ssl_key = </etc/ssl/private/imap.example.org.key
}
local_name imap.example2.org {
  ssl_cert = </etc/ssl/certs/imap.example2.org.crt
  ssl_key = </etc/ssl/private/imap.example2.org.key
}

-- 
Best regards

Gabriel Kaufmann