In Meir Shahar's The Shaolin Monastery: History, Religion, and the Chinese Martial Arts, there is a whole chapter (number six) dedicated to that topic. It basically debunks this (with reference to studies and historical sources) as a myth that had been raised as late as the 17th century and later. The conclusion ends as follows:
The seventeenth-century transformation of bare-handed fighting was accompanied by the emergence of a novel martial arts mythology. Shaolin monks
gradually accepted a legend that had originated outside the monastery according to which their fighting techniques had been invented by the Chan patriarch Bodhidharma. The legend of the Buddhist saint evolved in conjunction
with the myth of a Daoist immortal. As the “External” Shaolin martial arts
were attributed to a Buddhist master who reputedly resided on the sacred Mt.
Song, an “Internal” school of fighting was ascribed to a Daoist recluse who sup-
posedly hid on the holy Mt. Wudang. The two legends matched each other in a
perfectly harmonious mythological structure, the flawless symmetry of which
has likely been the source of their ongoing appeal. (p. 181, emphasis mine)
The main point is that while (apart from the questionable historicity of the person) Bodhidharma is seen as the spiritual father of the monastery, there is no evidence that there was any influence regarding martial arts (or, for that matter, that "he" even was proficient). It is only in modern times that stories were made up to provide a unity of religion and martial arts that provided further credibility and myth to the alleged superiority of (Shaolin-)Kung Fu.
The monastery itself was most certainly founded by an indian-born monk "in the last decade of the fifth century" (p. 9), while the first archeological hints to Buddha are from 728 and 798 respectively (p. 14).
Martial arts came into focus a long time after founding.