Yes, they can; you need to be employeed here with an EP/PR (duh) and you need to apply for permission at the Ministry of Education, but I gather this is just a formality -- which, however, will cost you S$5000.
That said, not many expats opt to put their kids in local schools. The local education system is grueling, with heavy emphasis on studying for tests and outperforming everybody else so you get in the right stream for the right school and the right university etc -- obviously this turns out little droids capable of absorbing and vomiting out vast amounts of information, but with no capability for innovation or risk-taking.
The flip side is that (after that initial hit) the rest of your kid's studies will cost S$3-5/month, while
International Schools are ludicrously expensive.