Is Gauss's theorem applicable to non-uniform electric field?

Now in all of these diagrams, the charge q$q$ enclosed in the Gaussian Surface, is always as the center of it. Thus the electric field is uniform throughout the inside of this Gaussian Sphere. But what if the field is non-uniform on the inside of the Guassian Sphere (in other words if the point charge is not at the center of the Gaussian Sphere? Does (1)$(1)$ still hold in that case?

Is ΦE=∮E⃗ ∙dA⃗ =Qenclϵ0  ${}_{}$ΦE=∮E→∙dA→=Qencl/ϵ0   still valid for non-uniform electric fields enclosed within Gaussian Surfaces?

Take the following example:
Example: A point charge q1=3.80nCq1=3.80nC is located on the xx-axis at x=2.1mx=2.1m and a second point charge q2=−6.2nCq2=−6.2nC is on the yy-axis at y=1.15my=1.15m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r=1.55mr=1.55m?  

Would the total electric flux through the Gaussian Surface just be

As even though q2$q_2$ is contained within the Gaussian Surface, it does not lie at it's center
Regards