No, this is not always the case, however, a lot of white cats with blue eyes are. The gene responsible for the white coat is dominant symbolised with a W (for white, obviously). This gene masks the effect of all other colour genes, so a cat may be genetically black or red, but the white masks those colours.
As has already been noted, the gene responsible in this case is known as W, non-white is w.
WW (homozygous) will produce a white cat
Ww (heterozygous) will produce a white cat
ww will produce a non-white cat
The eyes of a white cat may be blue, non-blue (usually copper or gold) or odd (one of each). Blue eyed cats are more often deaf than white cats with other coloured eyes. This occurs during fetal development. After conception, the embryo splits into three primitive germ layers:
Endoderm – The innermost layer of cells which form the respiratory tract (except nose), digestive tract, bladder, and urethra.
Mesoderm – The middle layer of cells which form the connective tissue, bone, cartilage, muscle, blood, blood vessels, kidneys, peritoneum, gonads.
Ectoderm – The outermost layer of cells which form the claws, hair, pigment cells, nervous system, eyes, and ears.
As you can see, the ectoderm forms the pigment cells and the eyes and ears. It seems in blue-eyed, white cats, there is a developmental fault in the ectoderm which results in deafness.
It should be noted that if a cat with odd eyes is deaf, it is always on the same side as the blue eye.
Deafness is more likely to occur in white cats with blue eyes, however, that is not guaranteed. A survey of 185 white cats reported the following results:
25% of white cats with yellow eyes have normal hearing.
31% of white cats and blue eyes had normal hearing
7% of white cats with yellow eyes were deaf
37% of white cats with blue eyes were deaf 
Are white cats albinos?
The gene responsible for albinism is different to the W gene. Albino cats are generally not deaf. There are five known albinism alleles in cats; full colour (C), Burmese (Cb), Siamese (Cs), blue-eyed (part) albino (c/a) and pink-eyed albino (c/c). Whenever you see a letter in capital form, it is a dominant gene, lower case is recessive.
Albinism occurs when the coat contains a reduced number of pigment cells (melanocytes), whereas non-albino white cats have the “normal” number of melanocytes, but they have been masked by the W gene. The part albino (c/a) will have pale blue eyes, the full albino (c/c) will have pink eyes.
White breeds of cat:
Domestic (shorthair and longhair)
Norwegian Forest Cat
Testing for deafness:
If you suspect your cat might be deaf in one or both ears, your veterinarian can organise a BAER test. This stands for brainstem auditory evoked response and detects electrical activity in the cochlea and hearing pathways.
White cats are at greater risk of sunburn and developing skin cancer. Not only that, but their deafness puts them at even greater risk of predators and cars. They should only be allowed outside in an enclosure or on a leash.