While I would agree that servers (regarding physical hardware) are not usually the best choice for digital signage as the Video Cards are usually not up to the standard, they can be used. But usually a desktop is just as powerful and would probably be a better choice depending again on the content used. It ultimately comes down to personal preference.
As for the 32-bit route vs the 64-bit, yes currently Adobe Air only supports 32-bit. But down the road, who knows. Why not get the 64-bit and the price is the same. Then when/if they do make it to the 64-bit world, you will not have to pay for an upgrade.
I say you get what you pay for, because it usually is true. I for one am always looking to find the most inexpensive route when I can. Who doesn't like to save money? I also use and support lots of open source software, but I also know that there are limitations to it as well. So, if you needed brain surgery, who would you trust the most, The surgeon at a world renowned hospital that charges you $500,000 or the surgeon down the street who is willing to do it for 10,000? In the end, it comes down to using the right tools for the job so that your client's expectations are not only met, but exceeded. What is your value proposition that you bring to the table, because there will always be someone willing to do it for less.
I am not sure why you would think the Android platform is "crippled", or why it would be better then Windows? MS was able to give you an added value, and OS that you can additionally use in your arsenal to support your clients. This currently is not their main platform. Maybe one day it will, but right now, it is just an added benefit. Everyone what's to circumvent the system to try and do it cheaper, then complain when it doesn't work on their home built machine. Android is an animal of it's own, which is why developers are not very fond of the environment. You have to build multiple versions of the app in the hopes it will work on the majority of them.
Going back to the OPs original question, I am not sure how the Thin Client would work out. It may be fine and I would not think it would be much different than the cat-5 extenders with the exception of the ability to be off site were range would be an issue for the extenders. I am just not sure how the video card of each device will handel it. I would be curious myself to hear any experiences, good and bad.