That's a pretty broad question - yes, there is at least one company I know of that has implemented a PMS integration to Conneciton using CUPI.  If you can do it depends very much on what features you want to implement, of course - "PMS" assumes a pretty standard set of base features but many do very specific things in specific setups so one can't really make a blanket "yes, whatever thought you have about what PMS means, you can absolutely do it with CUPI" here.
 

Q1 Open/create Mailbox for guest (CheckIn),
A1 - You would use the CUMI to do mailbox related queries.
CUMI docs are here - http://docwiki.cisco.com/wiki/Cisco_Unity_Connection_Messaging_Interface_%28CUMI%29_API
Also check this blog post - http://developer.cisco.com/web/cuc/blogroll/-/blogs/using-cumi-as-administrator-to-look-at-user-mailboxes?_33_redirect=http%3A%2F%2Fdeveloper.cisco.com%2Fweb%2Fcuc%2Fblogroll%3Fp_p_id%3D33%26p_p_lifecycle%3D0%26p_p_state%3Dnormal%26p_p_mode%3Dview%26p_p_col_id%3Dcolumn-1%26p_p_col_count%3D1
Q2. Close mailbox ,archive and clear voice messages (CheckOut),
A2 - The CUMI can be used to do this.
Q3. Edit GuestName,
A3 - The CUPI will help you do this - 
How to see the details of a user - https://<UCXN-Server>/vmrest/users/6eed4b74-41b2-4a92-870c-639c81f81a72
How to see a list of users - https://<UCXN-Server>/vmrest/users
How to modify user settings like language - http://docwiki.cisco.com/wiki/Cisco_Unity_Connection_Provisioning_Interface_%28CUPI%29_API_--_Examples_of_Basic_Operations#Modifying_a_User

Q4. Change mailbox password,
A4 - Use the CUPI for this.
Q5. query count of messages (read and unread)
A5 - Use the CUMI to do this. There is no easy way. You have to open the mailbox and read to the end. We are lookign at an enhacement to get a single query to get the counts with the release targetted for Summer 2013.
 
The CUPI is for the Unity Connection only. Will not be impacting CUCM.