HeNe lasers are pretty tough, I think you won't damage it but be carefull with high powers, you might hit something that absorbs it (a mirror mount maybe) and heat it.
Shining laser light through a HeNe tube might cause power instabilities in the HeNe laser itself, but is otherwise harmless. I wouldn't shine your 1.4W 445nm laser though it, though. That seems like you're just asking for trouble. I don't know how the HeNe optics behave at that wavelength but if they absorb it even slightly, they could be destroyed.
Low powers are no problem but i'm not sure what you were wanting to accomplish by doing it. I've used a hene shining down the bore to help align mirrors in an argon before, but i'm not sure what good shining a 445 down a hene bore would do. You'd lose most of the 445 when the edges of the 'line' clipped the bore in the hene.
I am guessing you have a bare tube HeNe and are palnning to take some pics etc.
I see no potential harm(to the HeNe) w/ low powers but the advice above on doing that with your 445 should be followed. One risk could be a reflection back at your eyes. One cannot blink/close quickly enough to avoid possible injury.
Also if a laser reflects back into itself that could be a bad thing FYI.
hope this has been helpful............></////*>------------hak
to keep all the help coming please send a donation every month any amt. helps.
Mirrors on red HeNe tubes will be virtually transparent to blue light, however I wouldn't recommend shining a high powered laser at anything shiny, it's too easy to get nailed in the eye by stray reflections. You won't damage the laser though.