Check this last part of this post, this should answer your query.
http://exchangeshare.wordpress.com/2009/07/07/how-to-setup-read-only-mailbox-in-exchange-20032007/Its pretty simple to add and open any mailbox in Outlook but how to open it in OWA? Reason is OWA requires Full Mailbox access to open full content of OWA site, otherwise it gives an error telling that you don’t have permission to access mailbox, so what you can do in Read-Only mailbox case?
Sometime back I discussed how to open shared calendar in OWA and user can use same method here to open “Inbox” of any read only mailbox.
User can use below direct links for respective folders and give their own user id and password to open it in OWA.
Inbox
https://<FQDN of server>/owa/<smtpaddress>/?cm
d=contents
Subfolder of Inbox
https://<FQDN of server>/owa/<smtpaddress>/?cm
d=contents
&f=inbox%2
fSubFolder
Calendar
https://<FQDN of server>/owa/<smtpaddress>/?cm
d=contents
&module=ca
lendar
Contacts
https://<FQDN of server>/owa/<smtpaddress>/?cm
d=contents
&module=Co
ntacts
Tasks
https://<FQDN of server>/owa/<smtpaddress>/?cm
d=contents
&module=Ta
sks