For mesons, or baryons, do sea quarks contribute to the angular momentum of the bound state? The total angular momentum of a bound state of quarks, such as a meson say, can be done by studying the spin and orbital angular momentum of the 2 valence quarks.
What about the sea quarks why they do not contribute? or do they? 
 A: I will tackle the experimental part leaving the theoretical for the adepts of QCD on the lattice, as the link dmckee  provided in the comments clarifies.
This is a picture of a gluon and a quark antiquark pair, in OPAL.


Gluon-jet studies developed into a precision technique for testing QCD at LEP. In this event from the OPAL experiment, the most energetic jet (going to the bottom of the picture) is likely to be the quark that didn't radiate a gluon. The jet moving towards the top right can be identified as a b-quark jet, because an energetic muon (red arrow) was produced in the decay of the b-hadron. This leaves the third jet as the gluon jet and permits the comparison of the properties of quark and gluon jets – an important test of QCD.

The corresponding Feynman diagram is 

We see here that out  of the blue, the energy inputed by the incoming electron positron pair becomes an offshell photon ( spin 1) and a quark antiquark pair (spin 1/2 each) , with a gluon (spin 1) emitted from one of them . The total angular momentum must add up to the spin of the photon that gave birth to them. 
Note that by quantum numbers the three end products could be within a bound meson, if the energy were lower. The algebra is the same. 
you say:

The total angular momentum of a bound state of quarks, such as a meson say,

We know just the total spin of the meson, because we have measured it, not how the quarks and gluons inside add up to give the measured value. For example the quarks could add up to zero spin and the spin observed be the spin of the gluon, in the picture above. In a pion which has zero spin all  spins must add up to zero. The total spin does not tell us any details about the internal spin form factors unless we do specialized experiments as in the link above. 

can be done by studying the spin and orbital angular momentum of the 2 valence quarks.

Do you have a link for this? We only have measurements for the  spin of the bound states of quarks. The quark model does not depend on the quark spins except as a limit in conservation of angular momentum .
For example in the meson octet:


The meson octet. Particles along the same horizontal line share the same strangeness, s, while those on the same diagonals share the same charge, q.

The spin does not enter in the symmetry pattern classification, it characterizes the whole representation.

What about the sea quarks why they do not contribute? or do they?

Logic says that they must since angular momentum is not like charge and strangeness, simply additive. 
