By definition, you can't "ride english" in a western saddle, just like you can't "ride western" in an english saddle, or ride side-saddle in a normal saddle. However, there's no reason you can't RIDE it a western saddle, but if you're going to be doing "english things" (such as dressage work and jumping), you really should get an english saddle. Different saddles have different purposes, and a western saddle will put your body in a position different from that of an english saddle.
Also, I am very against jumping regularly in a western saddle. It isn't made for it from the horse's point of view (I would say frequent jumping in a western saddle is quite detrimental to the horse, although I'm sure occasionally and over low jumps there's no harm), and definitely not made for jumping for the rider, either.
If you're serious about riding english, you should get an english saddle. However, as long as it fits you and your horse, it doesn't have to be a super expensive, nice saddle.
Also, you should not direct rein your horse in a western shank bit, period. Especially when jumping. It is made for neck reining, where the major effects of the turning aids through the reins are applied to the horse's neck, with only residual effects on the lips,bars, and cheeks.