Correct, although reaching "space" for SS1 will mean burning the engine for about 20 seconds longer. That's not too difficult for such a lightweight vehicle- there isn't as much of a weight spiral like in larger vehicles.
The SS1 doesn't have a heat shield, but heat is still an issue on a suborbital flight, due to the high Mach numbers reached during the ballistic descent. Rutan got around that by designing the feather position, which causes a lot of drag, and allowed him to use standard composite construction for the fuselage and plastic windows (although he did have to use polycarbonate windows instead of acrylic, because there will still be some heat).
The heat caused by a return from orbit would be another matter, since the vehicle needs to decelerate from 14,500 MPH to landing speed, and does so by converting the speed to heat. Even if it could carry the fuel, the SS1 wouldn't be a practical design for orbital flight, because the thin composite tail structure would be impossible to protect from the heat.