syllable-word nonalignment

I had a morphophonological idea while walking to campus the other day.  One
might have a language with, say, maximal CVC syllable structure, but in
which typical words are composed of CCV units, which are syllabified by
transferring the initial C of each word into the syllable of the final V of
the last word: so /ba tgude mdaska lti/ [bat .gu.dem .das.kal .ti] or
whatever.
Maybe syllable boundaries by themselves aren't detectable enough to make
this interesting: so you might have some ramification of the syllable types,
like weight-dependent stress, that is ordered following this C shunting; or
you might have VC pairs that react when they come in contact in a syllable;
or you might have occasional word-final Cs that, when they get a C shunted
onto them by a preceding word, invoke syllable-internal cluster resolution
rules yielding sandhi-type outcomes, which sandhi would fail to happen
across heterosyllabic junctures.

Is there ANADEW for this, or anything like it?  Anyone done something like
this in a conlang?
For that matter, is there some theory that says that this sort of thing
shouldn't ever happen?  (I don't know what consequences the phonological
word has in practice, but I could well imagine that it might not find this
copacetic.)

Alex

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