The Picard Maneuver definitely assumes a lot of things, and I imagine that if actually executed it would have a low probability of success (of course, he was going against Ferengi, so FTW!)
However, the base assumption is that the battle is taking place at sublight speeds in relatively close proximity. Ships are firing at each other using phasers. I don't have details on FTL/subspace sensors, but it is probable that they are not monitored or in use when engaged in a local firefight. For example, I don't look at my GPS when the Chipotle I'm looking for is across the street. Sublight sensors would indeed be fooled for a split second by a ship suddenly warping to another area of space.
This is all destroyed by the fact that phaser fire presumably moves at the speed of light itself, so by the time you noticed the ship wasn't there anymore you'd also notice that you'd been fired upon.
EDIT: Oh, I forgot that the specifics of the Picard Maneuver require that you warp TOWARDS the enemy vessel (and not merely a sideshift), so if you're able to do that and fire instantly, yeah. They're probably screwed.