The answer is "yes". The area you cannot access is Space Station 2, as time trial mode calls it. Every yellow area on this map that you cannot access is part of Space Station 2.
It could be confusing however because Space Station 2 shares a few rooms with Space Station 1 (like "B-B-B-Busted", where the area below is simply a harder version of Space Station 1) and also has yellow color. The most noticeable example is "Exhaust Chute", where you simply fall in Space Station 1 and have to use moving platform in Space Station 2.
In fact, you can access Space Station 1 from Space Station 2 by falling up. It's not possible the other way because of spikes (unless you use invincibility mode, but that's not available in the demo).