Are orbiting masses in a uniform disc affected by masses outside its orbit?

To answer I would use gauss theorem: $$ iint_{S} vec{g} cdot d vec{S}=-4 pi G iiint_{V} rho_{m} mathrm{~d} V=-4 pi G M_{mathrm{int}} $$ Assuming the disk is a very thin cylinder we could write $S$ as: $$ S = S_{top} cup S_{bottom} cup S_{side}$$ Splitting the first integral you'll obtain terms not equal to zero: $$LHS = 2pi R e g + pi R^2 g + pi R^2g $$ If $e$ is the thickness of the cylinder: $$2pi Rg(e+R) = -4pi G (pi R^2e)$$ This gives us: $$ g = -frac{2pi GRe}{e+R} $$ So I would say the outside doesn't affect the inside but I'm very skeptical on my own answer:

1. I remember applying Gauss theorem in non spherical case can be tricky
2. I hadn't use this theorem for a while so I'm not sure about the computation

However I'm very interested by your question because I'm currently having an interest for MOND theory, I'll follow this.

Are orbiting masses in a uniform disc affected by masses outside its orbit?

Yes.

The gravitational potential inside a massive ring or annulus (in the plane of the ring or annulus) is not uniform. There is no “Ring Theorem” similar to the Shell Theorem. Since the potential is not uniform, there is a gravitational field from the outer mass.

The potential inside a ring can be calculated in the usual way by integrating $-G,dM/r$, the potential due to each infinitesimal mass $dM$ along the ring. For a ring, you do a one-dimensional integral around the ring in terms of an angle $theta$. The distance $r$ between the mass element and the position where you are calculating the potential is a varying function of $theta$ (except at the center). The integral is messy; it can be expressed in terms of $K(k)$, the complete elliptic integral of the first kind. It doesn't seem important to give details; the point is that the potential turns out to be a function of the distance from the center rather than a constant.

An annulus can be treated as a collection of concentric rings.

There is apparently a result due to O. D. Kellogg that says the potential within a uniformly-charged ellipsoid is quadratic. Wei Cai gives a closed form (eqn 80 & 83) for the potential within a uniformly-charged thin oblate ellipsoid (i.e. similar to a uniformly charged plate and perhaps equally relevant). This leads to the result that the field is given by $crhopi^2r/a$. Here, $rho$ is the density, $2c$ is the thickness of the ellipsoid and $a$ is its outer radius.
If I'm interpreting this correctly, it says that the field varies linearly with radius, r, inside the ellipsoid, but inversely with the outer radius. This result seems a little surprising. It does seem to say that the field at a given radius will drop as material is added outside that radius. So this differs from the result for a sphere.