They absolutely could have built a digital computer and much more. He's slightly underestimating Roman enginuity for delicate manufacturing. Consider for example the Cage cup[1]. It's an exquisite piece of art and creativity and, all things cosidered, engineering as well due to the very tight tolerences and detail.

There's a lot more to progress than just the capacity for great leaps in engineering and sciences. Often times, there's a bit of luck and timing (Newton's apple and, of course, Newton himself) and also a societal willingness to promote new kinds of thinking.

The Antikythera mechanism is thought to be more a Greek invention than Roman[2]. And I've felt the Greeks were more appreciative of experimentation than the Romans who were driven more by the necesities of war and maintenance of the empire and they may be better candidates (with perhaps some Roman help) to go about making a proper computer.

We also need to understand that certain concepts in mathematics didn't exist in Roman mathematics at the time, like Zero (before Ptolemy)[3], which in addition to meaning "nothing" as quantity it also means "something" as a value.

We also know the Romans traded extensively in the Middle East which means they could have potentially been exposed to very early experiments with electricity[4]. While the age of "Bagdad Battery" like devices are debatable, it's not too much of a stretch to see ancient alchemists experimenting... more than likely the Greeks.

  [1] http://en.wikipedia.org/wiki/Cage_cup
  [2] http://en.wikipedia.org/wiki/Antikythera_wreck
  [3] http://en.wikipedia.org/wiki/0_(number)
  [4] http://en.wikipedia.org/wiki/Baghdad_Battery