The bottom line Okiale is, that so long as you were clad in your Tefillin even just for a split second, you have fulfilled Torah obligation of Laying Tefillin for that day. … This that we ordinarily lay Tefiilin in conjunction with prayer time; i.e. Schacharis or Mincho on Tish b’Ov, certainly doesn’t in anyway absolve you from laying Tefillin simply because you cannot pray before going to work.
In theory you also shouldn’t eat before laying Tefillin; Hence a good reason to lay Tefillin in morning even if you don’t have time to pray; Needless to say, even if you did eat, you still have a Torah obligation to lay Tefillin, and still recite the applicable Berochos for laying Tefillin.