No, the shot X does not carry from ball to ball, so it provides a decent risk/reward of use it or lose it. But as previously mentioned by others, good luck not accidentally using it during a multiball.
I don't know about the impact of a successful inlane X on one Arena shot and if it builds into subsequent Arena shots. My guess would be that it doesn't have an effect. But if you loop Arena again after the successful inlane X shot, you'll still get your natural multiplier on the next Arena shot that's built into the mode's logic.