Can cat allergies be overcome?

Yes.

All I can provide here is my own situation:

I personally have been tested for allergic reactions to cats.  I test HIGHLY positive to cats (and ragweed).  This test was done by a allergist, in a hospital.  I own four cats, and never sneeze, and never have watery eyes.  I must admit though, if I am scratched during a play fight, yes, the scrape does swell up, and it takes longer to heal than a 'regular' cut.

I asked my allergist about his, questioning his diagnosis.  His response stated two things:

• From a medical standpoint this makes no sense
• He had heard of this 'situation' before

I appreciated my allergists' honesty. I agree that chemically, if I get 'cat' into or on my blood I react, yet I feel no sneeze urges, nor any watery eyes.  This leads me to believe there is A LOT that medicine does not fully understand about allergic reactions.

My advice to you would be to 'try' a specific cat. Rub your face into it, see if you react. I am very lucky with my four cats, I hope you are too.