1) Is my math correct?
In so far as it goes, yes, it is. However, see the next point:
2) Since each state has a specific, non-random number of electoral votes, could this situation arise?
The number of electoral votes each state gets changes every 10 years. Each state has a minimum of 3, so in theory there would be some combinations that could never happen (such as 537-1). However, two states (Maine and Nebraska) award an electoral vote to the winner of each district in the state in addition to one for the overall winner, so it should be possible for every numeric combination to happen.
However, the vote of a state is largely influenced by its demographics. So there are certain combinations of votes which are exceedingly unlikely to occur in reality (within any given election - demographics change between elections). That said, not having a winner declared with one state left to report is a very feasible situation - that's what happened in 2000. From Wikipedia:
As the final national results were tallied the following morning, Bush had clearly won a total of 246 electoral votes, while Gore had won 255 votes. 270 votes were needed to win. Two smaller states—New Mexico (5 electoral votes) and Oregon (7 electoral votes)—were still too close to call. It was Florida (25 electoral votes), however, that the news media focused their attention on. Mathematically, Florida's 25 electoral votes became the key to an election win for either candidate. Although both New Mexico and Oregon were declared in favor of Gore over the next few days, Florida's statewide vote took center stage because that state's winner would ultimately win the election. The outcome of the election was not known for more than a month after the balloting ended because of the extended process of counting and then recounting Florida's presidential ballots.