Yes, a "Mail Alias" translates to an MX record. The reason for using MX records is that it is faster for delivery. All compliant SMTP delivery programs check for an MX record first and the A record second. So it's good general practice to have MX records for all addresses that might appear as part of an e-mail address.
Regarding a "regular alias" (a CNAME record), that's a different beast. If a name is associated with a CNAME records, there should be no other types of records for the same name. So in this case, there can be no MX record. Using cgl as an example, we have:
mail.cgl.ucsf.edu CNAME cgl.ucsf.edu
cgl.ucsf.edu MX cgl.ucsf.edu (priority 0)
cgl.ucsf.edu A 169.230.27.20
So mail can be delivered to either "conrad@cgl.ucsf.edu" or
"conrad@mail.cgl.ucsf.edu" (I think). In the both case, the
mail delivery program should query for MX(whichever name), and
send it to 169.230.27.20 (the A record is sent as part of the
MX answer). If the MX record were missing, it would get an
answer of no MX; at which point it would query for A(hostname)
and send it to that IP address.
It's a minor detail, but does make things work marginally better.