Okay, I was thinking a clogged artery could decrease BP..
Symptomatic arterial thrombus is relatively rare in the upper extremities.
If you think about it, most arterial blockage is due to atherosclerotic plaque which tends to, almost exclusively, cause blockage in small arteries such as the coronaries long before it could affect large arteries like the axillary or radial artery. Also, emboli from the legs or elsewhere would tend to be caught in the lungs (the dreaded P.E.) before they could ever get to an artery in the arm, with some exceptions for people with septal defects allowing paradoxical embolism.
There are a few possible exceptions, I've seen a few articles talking about things such as thoracic outlet syndrome, cancer, and some congenital hypercoagulable states(more commonly affect veins) mentioned as possible causes for upper extremity arterial occlusion.
Upper Extremity Arterial Thrombosis
Hypercoagulable disorders
Interestingly, 9% of patients (for lack of a better term) in an autopsy series were found to have left subclavian stenosis or occlusion.
Subclavian Artery Thrombosis
Aortic dissection can affect the subclavian artery as well, possibly resulting in decreased blood flow.
Aortic Dissection
However, depending on the artery affected and the amount of collateral circulation, and your skill in taking an accurate BP, I don't see why it couldn't cause a unilateral decrease in upper extremity BP. It just wouldn't be at the top of the differential for different BPs in the arms.