Uncorrelated but overlapping spectrum.
If you mean correlation at the origin (no signal shifts), then yes so long as all the overlapping frequencies the two signals are 90 degrees out of phase. 

That is, for all positive $\omega$ that are overlapping, $h_1(\omega) = k_\omega h_2(\omega) e^{\pm i \tfrac{\pi}{2}}$, where $h_1$ and $h_2$ are the spectrums and $k_\omega$ is just a real scalar. The negative frequencies will be the conjugate of these.

If you mean correlation with signal shifts (cross-correlation - similar to convolution) then no, because if both signals have the same non-zero frequency then at some shift the sinusoids will not be 90 degrees out of phase, and therefore correlated.

More simply

Imagine a signal consisting of a sine wave and another consisting of a cosine wave of the same frequency. They will have overlapping spectrums (same frequency) but have zero correlation.

Add to the first signal a sinusoid of a certain frequency, and add to the second signal the same sinusoid but 90 degrees phase shifted.

Example

Barbara image with DC component removed, and Barbara image with DC removed and half spectrum multiplied by $i$ and the other half by $-i$ (90 degrees phase shift and conjugate for the negative frequencies)

  

Their spectrums overlap completely but they have zero correlation (at shift 0).