Almost certainly not
The connection you mention is extremely tenuous at best. Apart from the common name “Ramsay” where one is the first name and the other is the surname the character/person are nothing alike. You mention Gordon Ramsay is a “sadistic bastard” but he isn’t really is he? He gets irate at incompetent chefs in a high pressure situation, I’d call that a short temper.
With that said George has been asked in the past if he based Ramsay on anyone and the response was a resounding no. I’m sure if he’d named him after the chef he would have spoken up about it given the opportunity.
Was Ramsay inspired by any real people George knows? Laughter from the crowd, and then, "No, not really," from George. More laughter.
Westeros, So Spake Martin, STOCKHOLM AND ARCHIPELACON REPORT