Alex,

http://sharepoint.stackexchange.com/questions/86072/sputility-sendemail-with-attachment-ics-files

As the above suggests:

> There is no possibility to send Attachments using this method. But you
> can use of SPAdministrationWebApplication to get the SMTP server
> details.

I'm not sure if SPAdministrationWebApplication is accessible in client object model.. Give it a try.. otherwise you might need to hard-code the email server address..