Questions:
(1) When I import a private key from Qt to Armory - the key (along with its funds) still also technically exists in Qt wallet.dat, right?
This way, if I make some mistake on the import to Armory, then my funds are still ok in Qt, assuming I don't lose my Qt wallet.dat file?
Yes
(2) I want to avoid "sweeping" - which I can't figure out how to do fully offline.
Actually, sweeping is recommended since when you export the private keys, you are at more risk of them being stolen. Sweeping makes sure that even if someone steals your private keys, there won't be any Bitcoin for them to steal. It won't work if you are offline.
So I want to do as follows:
(a) Import private key from Qt to a "temp" Armory wallet "TempWallet" (offline of course).
(b) Create another, separate "permanent" Armory wallet "PermWallet" (also offline).
(c) Import private key from Qt wallet.dat to Armory wallet "TempWallet".
(d) Offline-sign & online-broadcast a transaction (using the normal procedure) sending funds from Armory "TempWallet" to Armory "PermWallet".
Would this work?
It would, but it is a lot more work than necessary.
Now I know that you don't want to put the qt-wallet online again, but that may actually be the only way to get the funds from your qt wallet to armory. The problem is that bitcoin core uses compressed keys now and armory only supports uncompressed keys, so the keys from Bitcoin core won't be able to be swept or imported.