If anything it will decrease it because the vehicle will weigh more (GCVWR will be the same with a heavier vehicle). You need to add the 4k tow package to get more towing capability.
They are pushing the 4k tow package so they won't tell you the FX4 adds towing capability. You are getting upgraded suspension, heavy duty radiator, heavy duty engine cooling fan, different drive modes and hitch, not to mention another 59hp or so from the 2.0 and AWD. I guarantee this package with the 2.0 should allow the truck to tow at least another 1k pounds over a standard 2k towing of a FWD 2.5 Anyone who tells you differently is clueless and has little to no towing experience. The trans cooler is nice, but is an easy aftermarket add and the rear gear ratio isn't that different to really make a difference. If you are towing 3k pounds or under you don't really need the trailer brakes offered on the 4k package. If I had purchased the XLT I would have got the FX4 package and not the 4k tow package since all of my trailers are under 3k pounds. I couldn't get the fX4 on the XL. The FX4 package should be listed at 3k pounds towing capacity minimum from the factory. Shame on Ford.