Depends on how much cold work you want to do.  But yes, you will need to start thicker and have it rolled.  You are going to need a specialist to do it.

http://www.ulbrich.com/index.php/design/design/page/rolling_annealing.html

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.
 

You can find cold work curves for most materials in data sheets.
Often you are looking at 40-60% reduction in thickness to reach maximum hardness.

You do know that some of the PH grades can be made in the CH condition, where they are cold worked and then aged without annealing.  You get some added strength from the cold worked condition.  Look at 17-7PH.

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Plymouth Tube

I'll look for a datasheet, roughly speaking then I could buy 0.4mm 17-4PH annealed with hardness of 1000N/mm2 and any regular cold working to 0.2mm will get the hardness to approximately 1800N/mm2 (give or take a lot). It looks like a useful rule of thumb and sounds about right. I didn't know about 17-7PH, I'll take a look.

I wish I'd seen Ulbrich's online shop a couple of months ago. Seeing that was a revelation and a pleasant change from the prices I've had recently. I will call them, there isn't any PH stainless in the online shop but the prices give me confidence a special order wouldn't be too expensive.

Thanks.

Ant.