You mean using the same private keys? Yes you are essentially using the same "wallet". Another way to thank about Bitcoin is really you are not holding any "coins". All that you are "holding" is in the blockchain which you control through your private key.
Yes, the same private keys. Thanks for confirming my understanding.
So, in this scenario, I could send/receive bitcoins from either Armory installation, in any order, without any problems?
Yes, as long as you let both installations sync with the blockchain, they will see the transactions made on the other machine. The only thing you miss is any comment you have made on one machine, they will not appear on the other. And if you spend from one machine, and try to spend from another machine before the first transaction has confirmed, you may accidentally create a double-spend, in which case only one of the transactions will ever be accepted (probably the first).
