This syndrome affects many apneics.  Your blood pressure may actually be lower than your physician thinks because of "white coat" syndrome.

 see http://www.scienceblog.com/community/older/2004/1/2004258.shtml

'White coat hypertension' common among sleep apnea patients  

One third of sleep apnea patients diagnosed with hypertension may have normal BP

Excellent summary at above blog.  Link to journal article within blog article.
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Oh My.....Thank you so much for posting this.  Everytime I go to a doctor, they want to admit me to a hospital because my blood pressure goes so high!  I know its white coat syndrome as I have lived with it forever but sometimes it is hard to make the doctor understand that this is the cause of the reading.  When they take my blood pressure, it doesn't even "feel" that it is high.  My ears are not ringing, my head is not pounding etc etc.  The last reading of my blood pressure at a doctor was 196/140.  I monitor this twice a week at home because my reading at the office have been so high so I know this is not a normal thing but indeed "white coat syndrome".

The ER doctor I saw early yesterday morning confirms that.

She said they never pay much attention to the first blood pressure taken in the ER because the patient is usually quite agitated by their symptoms.

I actually did have hypertension thought due to severe, under treated Hashimoto's. After the doctor spoke with me and I told her what was happening with me, my BP went down to normal within about 30 minutes.