I doubt you can install Zarafa on shared hosting. Either they offer or they don't, and most hosts tend to offer Horde IMP and/or RoundCube instead.
Even if Zarafa was installed, it would have to be connected to an OpenLDAP server (to which Tiki would also authenticate against) and I doubt any shared hosting provider will offer OpenLDAP either.
Theoretically, an app like Tiki could authenticate against the e-mail system. This used to be possible in Tiki: IMAP Authentication. However, this doesn't feel very future-proof.
A 1 gig linode is not much more expensive than shared hosting: