Is there any way to have messages sent to a specific local address delayed by - say - 24 hours?

Set up a router like this:

delay:
  driver = redirect
  domains = the.domain
  local_parts = thelocalpart
  condition = ${if < {$message_age}{86400}{yes}{no}}
  allow_defer
  data = :defer: message not old enough
  no_verify

Of course, this will also have the effect of setting a retry time for the address. You may want to set a special retry rule for it. Note the use of no_verify to ensure that this router is not used when Exim is verifying addresses.