It is unknown at this time whether Phoenix uses the Halo engine, a modified Halo engine, or something entirely different. It is widely believed that it is either the Halo engine or something based on it.

Update:

After the cancellation of Phoenix, Matt Soell at Bungie was asked whether Phoenix used the Halo engine.

He replied:

The original basis was the Halo engine, but like Halo (which began as an evolution of the Myth engine) there were significant differences between Phoenix's engine and the original code.