You can't possibly hide something like a ship under construction. At least not from anything else in the same system.
Not in the same system as an Imperium planet, but just as an extra level of security over building a planetside base. Imperium scanners do have a hard time scanning asteroid fields.

I would say though, most Pirate shipyards will just be for refitting and fixing ships, rather than constructing them. Most pirate vessels will be looted, salvaged or turncloaks. The constructor ones...

And if the warp storms prevent jumping, how did they get there in the first place? (or still get customers if they were there before the storm was)
Warp storms don't really have predictable effects. The biggest haven for pirates in the galaxy is the Maelstrom, a region of warp storms rivalled only by the Eye of Terror, but not quite so Chaos dominated. It's hard to get in to those areas, but the navigators and crew know the tricks and routes that will let them pass in and out *relatively* unharmed, while IN ships would get smashed by squalls.

It is in these almost unassailable fortresses that great pirate empires arise, in lawless regions outside Imperial justice. This kind of area is where vessels intended for Piracy are constructed and purpose built for the task.

This makes more sense, but all it takes is one scout frigate to jump into the system and jump out before anyone else can catch it.
And then for a fleet of a dozen vessels to be dragged off from patrols and military work to scourge an area of space that is probably fortified, to attack an enemy who will probably have stripped their base bare and left before your fleet even arrives. If you get lucky and find the pirate fleet and they want to fight? Then they probably think they can win, and in attacking them in their home turf you run the risk of them capturing a dozen war ships to add to their fleet.