What happens if a city snakes to an outpost that has the combat/movement bonuses, etc?
I had it happen once while building my own 'superhighway' as Darxim calls it, and I noticed that the improvments (specifically stables) moved into the cities' list of buildings but honestly I didn't do much testing as to how it works, just wrote it off as weird and moved on.
EDIT: well that was interesting. Did some testing with Pariden and arcane monolyth and the basic attack/defense upgrades and it seems that if you snake to an outpost after building upgrades in it, everything works fine. the upgrades are in the list for the city as one of 'its' buildings, but in the outposts list too so you can't build them again. If you build an upgrade there after snaking to it it only appears in the list for the city, not the outpost and so you can build it again, an infinite number of times..... 
EDIT2: also, even though the building (eg, armory) is listed as a building that the city 'has' if you snake to it (possibly multiple times if you snake to multiple outposts, and the bonuses stack
) the effect is still only local to the outpost. Also stuff built after you snake has no effect, at all (I forgot to check that before my first edit)
Final note: Snaking only occurs (the outpost becomes included in the boarders of the city for the porposes of ZoC around the city, including the healing the land effect) if the outpost has at least one upgrade, or you start building an upgrade once snaking could occur, untill then the city won't expand it's boarders or put the graphical fence around the outpost.