I have had a few issues in the past when I have setup a website in a plesk shared hosting environment and used gmail hosted apps for the same domains email and not that which is offered from within plesk.
I setup up a DotNetNuke site in the shared hosting and then configured the smtp account in the host settings, send a smtp test and the email was received.
When I am expecting an email from the website from a contact us form or something similar, nothing ever arrives at my domain’s email account.
When sending a bulk email to myself, the bulk email report has the following failure message: “Mailbox unavailable. The server response was: No such user here”
What I have found is that when you are using a plesk control panel and Google hosted application (or live mail) for email hosting, I keep getting “Mailbox unavailable. The server response was: No such user here”
After checking the DNS a number of times I could find not find any problems with the DNS. What I have found is that even through you have removed or changed all the MX records to point to google apps plesk still has it’s own mx records that you cannot see.
The way to fix this problem is to actually disable the mail service for the domain from within your plesk control panel as the email that you are trying to send to your domain is actually intercepted by the local mail server for your domain. The email accound does not actually exist on the local mail server and then you get the “Mailbox unavailable. The server response was: No such user here” message.
I hope that this can help somebody as it was annoying until I worked it out!