So, say my website sells "Kool Aid" and is focused on Denver. This location would thus be mentioned frequently throughout the website, but my business is NOT located there. If someone located in Denver were to search for "Kool Aid" (but not include Denver in the search entry), would my website have an advantage (all other things being equal) compared to others which are 'more general' Kool Aid-selling websites?
That depends on whether "kool aid" (I assume this is a metaphor for your real keyword) triggers a local search algorithm. If Geolocation kicks in you're usually lucky to end up on Page 2 somewhere.
If you're targeting queries like "kool aid in denver", "denver kool aid", "kool aid for denver", "denver area kool aid" and those queries DO NOT trigger a Geolocation algorithm (i.e., you don't see the map and featured local listings) then you're probably on about equal footing with everyone else.
Then again, sometimes Google will feature a non-local business in a local query simply because more people click on the non-local business listing -- and that was recently confirmed to one marketer by someone at Google.
It's a crazy, mixed-up world out there. Good luck storming the castle.