If a runner makes a card ability run on a server with crisium grid, can the corp play successful demonstration? Trying to wrap my head around the wording of both cards and how they interact.

It depends when the run ends. If the run is successful, then Crisium turns it into neither successful or unsuccessful. In this case Successful Demonstration can't be played.

However if the run ends without success, (I.e. The runner never reaches the correct stage of the timing structure where runs are declared successful), then Successful Demonstration may be played as normal.

Don't feel bad about not being able to wrap your head around it. It breaks a fundamental law of logic.

http://en.wikipedia.org/wiki/Law_of_excluded_middle

In a perfect world a run which does not complete successfully, necessarily is Unsuccessful. If I were king, you could play Successful Demonstration after you RFG Jackson Howard mid-run, and Crisium Grid would get errata that runs are considered Unsuccessful for card effects.

We've got to deal with the niceties of "vacuous truths" when dealing with whether Komainus and Woodcutters are broken whilst they have zero subs, it infuriates me that something even more foundational is flouted.