Firstly, I completly agree with dgillette, primary strength is almost meaningless in evaluating the behavoir of a rock mass. Bedding, joints, schistocity, water pressure acting in these features and the quality of any/all infill materials (i.e., clay) have a much greater affect then the strength of the intact rock mass.
On the more basic geometric question, the answer is, no but close. If you perform an unconfined compressive strength test you will get a maximum deviator stress for some failure criterion. That maximum deviator stress is the diameter of a Mohr's circle. So half of that value is some measure of shear strength for some measure of normal loading.
Cohesion is the shear strength for a normal load of zero. You can't determine the shear strength for a normal load of zero when you are performing a test that includes a normal load reaction. Just because sigma3 is zero doesn't mean that the normal load is zero.
If you consider the P-Q plot of a unconfined compressive strength test (or the stress path to failure), you will have a point that falls on the line "alpha" not a point that falls on the line "phi". These are geometrically related, but not equal.
Your question specifically related to rock. In soil, we have a parameter called "undrained shear strength". The undrained shear strength of a soil can be described by one-half of the unconfined compressive strength, but that's a separate topic.
Not to confuse that is. . . .
f-d
¡papá gordo ain’t no madre flaca!