The way cold storage works is by making the online computer generate an unsigned transaction, then making the offlline computer sign it.
Your issue will be with getting blockchain.info to actually generate such a thing. I've looked through their faq, and can't find info on how to do it.
Blockchain.info cannot create unsigned transactions of the form required for Armory offline-signing. You need to run Armory on both online and offline computers. The online computer can verify payments and monitor your wallet balance. You use online Armory to create the transaction the same way as you would with a regular wallet, but the output is unsigned. You get it signed by the offline computer before broadcasting/finalizing it.
I created a standard for this
(BIP 10) but no one else adopted it. Thus, you have to use Armory on the online system if you're going to use it on the offline system.
If I plan on only adding to my balance for the foreseeable future, and not spending (e.g., I am a long-term investor), could I still use the method that I outlined in the OP to have a watch-only wallet on blockchain.info (and by the time that I'm ready to spend, I'll have a third laptop (e.g., a second personally-owned laptop) onto which I can put Armory, and then use that as my online computer from which I can spend funds)?