No.
The Jolly Santa existed well before haddon Sundbloms famous 1930 advertising images.
His illustrations,and those of Thomas Nast in the 1860's,were based on New Yorker Clement Moore's 1823 poem " A visit from St Nicholas" (better known as 'The Night Before Christmas'
It moves the legend to Christmas eve,and,instead of the dour St. Nick,describes a rotund,twinkley-eyed,white bearded elf,with fur trimmed red clothes,reindeer with cute names a sledge that landed on rooftops and a sackful of toys
source
QI...The Book Of general Ignorance