[cobaltoxide]

Nope.

As a point of comparison, the orbital velocity of ISS is 17,000 mph.

The max speed of Unity was given as Mach 2.88. The speed of sound varies from 340 m/s at sea level to 200 m/s at 120,000 feet. So Mach 2.88 would correspond to somewhere between 1000 - 2000 mph depending on where it was attained.

To enter orbit, a vehicle must be simultaneously at orbital altitude _and_ at orbital velocity (in the correct direction).

Furthermore, note that quoting speed as a Mach number is fundamentally only relevant to atmospheric flight. Mach number is referenced to the speed of sound, and sound does not travel in the vacuum of space.

The Virgin Galactic vehicle shoots up to very high altitude but then simply falls back to earth.