You would have to run an email server on the same installation. If it's not possible to point MX for your domain to that server, you could use a subdomain.
Departments can override the from address as defined on the ticket, or not. If you only have 1 department, then you can disable the override on the department and mask the subdomain from the client.
For example: support@domain.com -> forwards to support@blesta-server.domain.com. This would be the Email set for the department, but the email templates would use support@domain.com and the department will not override the from address.
That is only useful if there is 1 department.
If you need more than 1 department that will accept email, then you can still forward email from your primary domain, but the from address must be overwritten on the department or replies will not make it back.
In this case, a customer may email support@domain.com, or sales@domain.com, and get a reply from support@blesta-server.domain.com, or sales@blesta-server.domain.com. For most people, this is not an issue. It may even be preferable to use a subdomain, or a different domain for tickets. You could use something like @companynamesupport.com for your ticket emails.
I hope that makes sense.