I just created an M-of-N offline fragmented backup paper wallet through Armory. I plan to put most of my BTC here. Before I do, I want to know that if anything should happen to Armory -- if they stop updating it, or I can't get it to run on my computer in 10 years, or there were some updates to Bitcoin-Core/the blockchain, or whatever -- will I still be able to get my coins out?
Short answer, you need Armory to open an Armory paper wallet.
I use Armory and it does not fill me with confidence. I set one up and it was taking forever to sync with the blockchain. I think it actually crashed. However I had bought some BitCoin which was in there somewhere but not showing. I made a paper backup and formatted the hard drive because the PC was playing up.
8 months later I discovered my Armory paper wallet saved as a PDF and decided to see if I could get hold of my BitCoin. The codes did not seem to be any use with any online tools I could find. It would not import into an online BitCoin wallet. I did not want to have to download the 140GB blockchain.
Anyway I did install Armory and activated the restore process for the paper wallet. It restored fine but seemed to be empty and I wondered why I had bothered saving an empty wallet that had never had transactions. The process of getting Armory properly running is like firing up a steam engine compared to turning the ignition on a car. I had to also install the normal bitcoin-qt in order to get the block chain. This took two weeks. Even then Armory was not happy. Several restarts later Armory had synchronized it's database and all the other nonsense it has to do. That took a couple of days or so.
Finally I discovered the wallet had £150 worth of coin in it! Dead chuffed.
I am good with computers but I found all of this hard work and stressful. The average person will need all this done for them. I'd put it on the same difficulty level as formatting your hard drive and re-installing the OS and all the drivers. Not the hardest thing in the world but beyond most people.
I'd say any sort of wallet you use needs to be backed up in a way that it can easily be examined in a couple on minutes rather than the 2 or three weeks it took me. It may well be down to my lack of experience but I did not get the impression that an Armory backup could be used on anything but Armory.
As a little rant I'd say Crypto has to get much easier than currently if more than just technogeeks are to use it.
What do you mean by "Armory ceases to function"? The software known as Bitcoin Armory is not a company, it does not "cease to function". If Armory were to become abandoned, then you could still download the software and recover your coins. Currently, Armory's backup and HD derivation stuff is all Armory specific, so you will need Armory in order to recover those coins. Even if binary distributions of the software are not available, its source code is. You can download the source code and build Armory yourself so that you can recover your coins. Note that all you really need to do is just get your private keys, and that does not require syncing the blockchain (so no Bitcoin Core).