Yes it's possible to develop apps on a machine without SLAT. It is not, however possible to run the emulator (in any kind of supported manner) on such machines.
It is possible to develop without an emulator though. You'll just need an actual device to test on.
This shouldn't be a barrier though because even if you have an emulator you should always test on a physical device. It's just a little bit more awkward to use a physical device sometimes.
On the plus side a physical device will let you test some things that the emulator can't. e.g. proximity
But on the downside the emulator makes it easier to test other things, like location changes or how the app will look on different resolution devices.