There is information on the web about doctors prescribing SNRIs (Effexor/venlafaxine in particular, but Cymbalta/duloxetine as well) off-label for migraine prophylaxis, so the short answer to your question is YES. They appear to be more effective in people with Depression or Anxiety disorders.

SNRIs for migraine

There is some concern about taking SNRIs (or SSRIs) and triptans (Imigran is a triptan -- sumatriptan) concurrently -- possibly resulting in a potentially life-threatening condition called Serotonin Syndrome. Cymbalta and Imigran/Imitrex/sumatriptan are mentioned specifically.

Public Health Advisory - Combined Use of 5-Hydroxytryptamine Receptor Agonists (Triptans), Selective Serotonin Reuptake Inhibitors (SSRIs) or Selective Serotonin/Norepinephrine Reuptake Inhibitors (SNRIs) May Result in Life-threatening Serotonin Syndrome

Shortly after this FDA Advisory was released, a mitigating article was published in Neurology Today and reprinted in ENT Today:

FDA Advisory on Triptans and SSRI/SNRIs Will Not Affect Migraine Treatment, Say Experts

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