Marcos, six weeks seems like a long time for your bird to be in
a splint. My cockatiel broke her leg years ago and was in a cast
for three weeks. My vet told me at the time that birds' bones
heal much faster than mammals, due to their metabolism and bone
structure. So you may not have as long a road as you think, as
your vet may decide to take the bandage off sooner, check with
him on this.
As far as; is it worth it, I'm not sure what you're referring
to, but if its' is it worth saving your budgie, definitely yes!
Since he is a pet bird who lives in a cage anyway, the ability
to fly is not a big deal if he doesn't regain it fully (which he
very well may). Actually it's not all that uncommon for pet
birds to lose a wing entirely due to injury or illness and
survive fine as pets.
I would stay the course and in the meantime pamper your injured
budgie as much as possible. If not already, get him some millet
sprays or a "honey stick" and put on the bottom of his cage for
him to enjoy.
As far as the biting, your bird has been through a very
stressful ordeal. For the first time in his life he was handled
in a painful way by humans while the vet was attending him.
This, of course could not be avoided, but it will take a little
while for the trauma to wear off and for him to trust hands
I think you are doing fine with him. Just pamper, give him his
time and I feel he will heal nicely, and possibly bond closer to
you in the end. I think animals have sense for when they are
being taken care of. My cockatiel who broke his leg, though mad
at first, ended up being my closest bonded bird.