I'm willing to go out on a limb and say yes, it applies the same way. A motorcycle is defined as a motor vehicle under Section 541.201(9) of the TX Transportation Code. Section 46.02 of the Penal Code allows unlicensed carry in a "motor vehicle" regardless of type, so strictly speaking, it appears to be legal.
OTOH I wouldn't do this on a motorcycle. The TX provision allowing unlicensed concealed carry in (or on!) a vehicle only allows the handgun to be carried when the operator is in (on) the vehicle or "directly en route to" it. The "en route" clause has been criticized for vagueness, but IMHO it's pretty clear that if one is
leaving the vehicle to go somewhere where a CHL would normally be required- e.g. a public place like a grocery store or a restaurant rather than one's own property- one is violating the provision. This is problematic because it is inherently difficult to secure a handgun to a motorcycle without illegally exposing it to public view.
Mandatory disclaimer: I am not an attorney, nor do I play one on TV. 
This is not official legal advice. Caveat emptor.