For maximum hold, the length of the thread is typically equal to the diameter.
I didn't see a design pressure or wall thickness on the tube, but it has to be thick enough to thread, so at least 0.110" wall.... I get about 3.5:1 safety margin on the tube at 5,000 psi, and about 25:1 for the threads on the plug at the same pressure.... At 0.40" thread engagement, it is still over 10:1, so IMO you have nothing to worry about....Bob