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So for example, taking mixolydian mode, the third of the vm7 chord (the flat seventh of the mode) is raised to create a V7 chord (as commonly occurs in tonal music in a minor key) which is then followed by the I.
How would this be interpreted? Would this chord be within the 'boundaries' of the mode?
By doing this, you're changing from Mixolydian to Ionian mode - the difference between the two being that 7th note.(Or 3rd. in Mixolydian).
I would say the piece is modal in nature but that it uses a tonal cadence to end the song. If the majority of the piece doesn't use V-I cadences, then the raised 7 (leading tone) is an exception. It is used to create finality. I relate this to the Picardy Third. When a Picardy Third is used the piece is still in minor and you need only make mention of it when you are describing the final cadence. The Picardy Third, if you don't know, was commonly used in the baroque period and consists of a piece in a minor key ending on a major I. ex: key of C minor: last chord is C major. A major chord is more consonant than a minor chord and the V7-I cadence feels more resolved with a major I. This is partly due to the desire for the 7th degree of the V chord to resolve down and the resolution by half-step is more solid. So, it gave finality in that it was more resolved than the expected minor chord (also a nice surprise in its early usage).
I digress... I would say the chord itself is not within the boundaries of the mode but the piece is.
It depends on how you're thinking about modal- from the perspective of the piece (or section of a piece) as a whole, or at that exact moment.
Looking at only the exact instance in which the leading tone is raised, no, it is not in the mode. However, looking at it in context, the section can still be considered modal, with the leading tone providing tension (it's a tritone away from the 7th of the V7 chord) that most likely resolves to a I or I7 chord.
As you said, this is common in tonal music in a minor key. It is also common in modal music. Take a look at Cannonball Adderley's solo on So What, which alternates between B dorian and C dorian. He plays A# over B dorian and B natural over C dorian several times, along with other notes that are outside the mode, but it it is still considered a modal piece of music. From the wikipedia article on modal jazz, "Kind of Blue [the album with So What] is an exploration of the possibilities of modal jazz."
http://www.cannonballjazz.com/Cannonball/1959/So_What_59-0302.pdf http://en.wikipedia.org/wiki/Modal_jazz
