I've been researching this pretty extensively and the answer appears to be "No (in most cases)."
Your "separate" calendar actually has its own EMAIL address. You can find this in the settings under integrate and it will likely have an address of:
???????@group.calendar.google.com (see screenshot).
The bad news: As far as I can tell, Google will NOT let secondary calendars auto-accept invites from an EXTERNAL address (i.e. a hotel, airline, your work address). This is bizarre and most maddening as it doesn't articulate this in the calendar settings page.
This issue is discussed in more detail on this thread. The calendar DOES auto-accept if it comes from a gmail account, however I haven't found an easy mail filter way to get this to work around the issue. An API will do it, but that's a pain.
Hopefully a solution is proposed. To me, the "least bad" workaround would be to create a separate google account, which is not ideal.
Feel free to send feedback to google via this link.