If you're using mySQL, if both users have full access to all databases, yes it will make a difference. If you've built the server yourself, and both users can peek at the other's data, and you've used the same database name (of course this implies that you have a single mySQL server) then each other's installation will update the exact same table on the exact same database.
If you had a more robust installation, you'd have a prefix on your databases names (ie: client1_calendar, client2_nuke, etc...) and the user client1 can only have access to client1_* databases and the same for client2..
This being said, you'll have to have (at the very least) a different name for your table. You can edit the table name by manually editing the file calendar.inc.php. An easier alternative (recommended) would be to have a seperate database.
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