This sounds like a postfix issue more than dovecot.

Its easy to make a slow deliever transport for postfix, many people do
so when sending emails to hotmail/yahoo.

Sounds like that solution would work for you, just applied to the
dovecot transport instead.

Quoting Maria Arrea <maria_arrea@gmx.com>:

Hello

We are running dovecot 2.0.13 with mdbox on RHEL 5.7 x64, ext4
filesystem. Sometimes we have a big load increase because a mailing
list server send 16.000 32k messages in less than 3 minutes. We want
to "slow down" delivery, we prefer slow delivery instead of logging
out webmail users.

I have the following line en /etc/postfix/master.cf:

flags=DRhu user=userid argv=/usr/libexec/dovecot/deliver -d ${user}

And in /etc/postfix/main.cf

mailbox_command = /usr/libexec/dovecot/deliver

I would like to add ionice to the equation, prefixing
/usr/bin/ionice -c2 -n6 before the deliver lines in postfix config.
Is there any other way of slowing down delivery speed vs imap access?

Regards

Maria