The possibility is there, yes, but the likelihood of it happening soon? Unlikely. World of ******** only in the last year has implemented the ability to work the Auction House remotely, and the game just celebrated it's seventh year anniversary. Coding something of that nature is innately complex, then tack on the fact that each sector block, exploration block, star system, etc. has its own "Current Sector" mission list, it makes things that much more difficult to code for remote DOFFery. Because of that, if they did do a remote system for DOFFing, you likely wouldn't be able to handle assignments outside of your last login point + current shipboard assignments. Granted, I'd be on board with being able to handle my DOFFing while on lunch at work and the like, but the reality is that, it's just unlikely we'll see something of this nature anytime in the near future.
I too would love to see an iPhone/Android/Blackberry(I can dream can't I) app that let us manage the non-ground/space aspects of STO. I'm talking Duty Officers, Dilithium Exchange, Banks, The Exchange, etc.
One of the Devs- I'm going to blame Gozer- said they would love to do it, but have issues with licensing and getting permission from CBS. There may also be technical issues because the missions that are available are based on your location. I personally would love to see an app.