
Probably not, depending on how severe the allergies.
There is a product called AllerPet for cats. Once a week you rub the cat with a towel soaked with the product. It helps to cut down on the dander in the coat.
Some people say that bathing the cat once a week in distilled water helps as well.
The problem is, you cannot make the cat NOT have dander. It's a natural by-product of its saliva when cleaning themselves. And not only does the cat have dander, but the dander will fall off the cat and into carpet, upholstery, etc.
I would worry about the stress on the cat - going to a new home, being soaked, bathed, etc frequently (which they can get used to), but then if it doesn't work, end up having to go to another home. Cats do not adjust to change as easily as a dog, and it can be VERY stressful to them. I see it every day at work.
Not to mention your family, and how attached everyone will be emotionally, then how painful it is to give away the pet.