The only controllers I would see being an issue are those that allow macro-mapping or those that can adjust to and "learn" to make one trigger pull the equivalent of several, in effect making any gun full auto. Not quite the same as the old turbo function, this is actually a better version of it.
As to the router, that heavily depends on how it's filtering works and how it responds to a game trying to match you with someone outside of whatever it's algorithm considers optimal connection range. If it just backs you out automatically, it's fine, if it does something to the other end of the connection, I wouldn't use it. But, considering destiny already uses a regional bias pretty heavily in its matchmaking, it should be an unnecessary feature.
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Thank you for responding!