Nope. Gas Safe is an organisation mandated by government which businesses and self employed people may join in order to comply with provision 3.(3) of the GSIUR:
"Without prejudice to the generality of paragraphs (1) and (2) above and subject to paragraph (4) below, no employer shall allow any of his employees to carry out any work in relation to a gas fitting or service pipework and no self-employed person shall carry out any such work, unless the employer or self-employed person, as the case may be, is a member of a class of persons approved for the time being by the Health and Safety Executive for the purposes of this paragraph."
It's the business that becomes a member of GSR (currently the class of persons approved for the time being by the Health and Safety Executive), not the individual.