Armory refuses to make a transaction that bitcoind or bitcoin-qt would refuse to propagate.
I send free transactions below the "rules" all the time on bitcoin-qt (Using createrawtransaction). They get confirmed after about a week or so, good enough for me.
Just to reiterate picobit's point: Armory's hands are tied on this one. You can use a modified version of Bitcoin-Qt to broadcast a tx to dozens of peers with sub-standard fee, and you are pretty comfortable that at least a couple of peers will accept and propagate. If you don't mind waiting, that's okay.
The problem here is that Armory doesn't have dozens of peers. It is connected to the network through exactly one peer: your own Bitcoin-Qt/bitcoind -- and one that is usually following the rules. When I first created Armory, I tried putting in a min-fee-override, but quickly found out it's pointless. The tx has to go through that bitcoind, and it will be DOA if it doesn't have enough fee for relay. 100% failure rate, guaranteed. So I had to disable it, because it was pointless, since 99%+ users don't have a setup capable of doing it.
Technically it can be done if you run a modified version of Bitcoin-Qt or bitcoind that will forward it in addition to modifying Armory to do it, which should be pretty easy. It's just that few people will actually do this so it's disabled.
Actually, if I'm honest, I don't even broadcast it through my bitcoin-qt, because if it does fail (I.E. nobody likes my cheap-ass transaction, and, it gets rejected and forgotten about by the network as a whole) it gets all pissy at me and I have to run the wallet through pywallet to get rid of the failed transactions (Assuming I want to modify them).https://blockchain.info/pushtxhttp://eligius.st/~wizkid057/newstats/pushtxn.phphttps://coinb.in/send-raw-transaction.html
Are a god send. I understand Armory can't use these sources (As some people won't want their IP being directly marked as "Creator of this transaction" by a centralized unit), but, I can.
Another idea would be, assuming you're in expert mode, you can overwrite the fees, sign it (Online/offline/whatever), etc..., then, instead of broadcasting, just receive a standard format rawtransaction that you can do what you like with.