Quasilinear Preference and MRS Do quasi-linear indifference curves have MRS's that depend only on the nonlinear variable?  For example, for a U(x) = √(x) + y, I calculated that the y would not be in the MRS.  Does that mean that a consumer does not factor the consumption of a "linear" good y into their utility maximization? 

If this is the case, can someone explain to me, practically, what it means for a good to be "linear" and for an MRS to exclude one variable?
The MRS is a function of $x$ and $y$. The fact that $y$ doesn't appear in the formula simply means that this function is constant in $y$. 

The linearity does not imply indifference. It means that an additional value of $y$ is valued equally by the agent irrespective of his baseline consumption. In your example, this contrasts with the marginal utility of consuming $x$ which is decreasing with the baseline consumption since the function $u$ is concave in $x$.