Thats a good question!  It is possible, but the only way i can think of doing it would be this:

1 - add your iocoin bittrex address, to your address book.

Name it something unique as you will have to attach a IONS name to it.

2 - (example) StrikeBittrex-io  or StrikeRex-io  or StrikeTrex-io  (you get the idea)

NOTE: As this name will be on the IONS, it will be publicly avilable.  You cna imagine if everyone wants to do this
they must remember to make it unique/

Then you simply create a new user name and attach your bittrex address to it.
Then when you want to send funds quickly to Bittrex, you can now use the IONS feature.

You can add any name to anywhere, this is the beauty of this feature.  The possibilties are endless.

REMEMBER: When using IONS all you need is a wallet adddress and you can create a unique user name for that and any address you wish (as long as the username has not been taken of course)