will having a high guage of strings such as .13 to .56 warp my 6 string neck and have to make me do a bunch of truss rod adjustments?
It depends what tuning your running. E standard with 13's you will have to adjust it.
E with 13's is the ****, the impossible to play **** that is. and if youre going from E with 10-46 and youre moving up to 13-56 id reccomend that you always keep it really detuned, like Db perhaps. and changing string gauges a lot or tunings a lot does indeed **** up your neck
You'll need to adjust the truss rod, yes. A tech could do it fairly cheaply if you don't want to.
why bother, though?