Do I need an MX record for my main domain?

Let's say I have several domains. bossguy.com is the domain that hosts my mail (IMAP server) and where I ssh in to manage other domains, for example:

• domain1.com
• domain2.com
• domain3.com

It makes sense to set up MX records for domain1/2/3.com to point to bossguy.com, so if someone emails me at whoever@domain2.com, it gets routed to bossguy.com for storage. But does bossguy.com need its own MX record (for emails sent to whoever@bossguy.com)? Currently I have it set up like this:

bossguy.com.     86400 IN MX 10 mail.bossguy.com.
bossguy.com      86400 IN A     23.xx.xx.xx
mail.bossguy.me. 86400 IN A     23.xx.xx.xx


Is the MX record needed in this case?

Also, assume all these domains share the same IP address. Then really, they could all just have MX records that equal the domain/host (domain1.com's MX being domain1.com), and it doesn't really matter since they all share the same IP. Correct?

If you send mall to example. com, and that name has an IP address but no MX, the sender has to ask twice (once for MX, which fails; again for A). It works, but adding the MX record is done as a courtesy to senders.