Application is still able to wait until you mistakenly switch to online. It can store all values in local storage and send them later.
At which point you're using the application online again. If you're trying to say "well we don't know if the application is secretly still running in the background", welllllll.. sure. But then there's a whole world of increasingly unlikely but certainly possible scenarios to explore

In each of them, you're using it online, knowingly or otherwise

When you paying?
Bitcoin has one big issue, which may make it unusable in the future. You cannot have easy-to-use true offline wallet. Because if you want to pay - spend funds - you need to go online, download all unspend outputs, then create transaction and sign it at offline, and then switch back to online and broadcast it. Every time you are going to online, there is a chance, that unwanted piece of software running in your offline wallet will get chance to leak your private key.
Alternatively you can use online computer and offline wallet and carry the request through no-internet medium, such a QR code, but it still need device with camera and display and it is not easy-to-use.
Bitcoin protocol need an improvement, which should allow to create partial transaction signed by the private key that allows to 3rd party spend your coins up to specified amount. 3rd party can be merchant. 3rd party can take any of your unspend outputs and create transaction to any address that he chooses, but only up to specified (and signed) amount (transaction should send rest of coins back to source address). Result transaction is finally signed by another private key... so you will need two private keys to create such a transaction, but second private key is used only to protect transaction against unwanted change. Second private key can be supplied by the 3rd party.
This can help to not only create true offline wallet, but to simplify money transfer between customer and merchant, Customer only needs HW wallet with display able to show QR code and keyboard to type amount and pin. Merchant will need online application to sign transaction and broadcast it.