On the face of it, it seems on-topic because it is about a web application and, further, would seem to have a definitive yes or no answer.
However, at best this sort of question will just attract a host of "yes, it's down for me too" or "no, it works for me" answers.
Beyond that, the majority of the utility of questions and answers is for the long tail: People who have the same issue and are looking for a solution. Asking a question about whether a service is down at the moment would have been a perfect case for the old "Too Localized" close reason, as being a "specific moment in time". (My goodness, imagine if we had questions from whenever Twitter was showing the Fail Whale.)
Had the example question been something along the lines of "What does this error mean" or "How can I confirm that Service X is having an outage or if it's only my account" those would be good questions.
But I think questions asking "Is Service X down" and similar aren't useful and should be eliminated.
The other question is is this enough of a problem to need a custom close reason?