Allow me to nitpickbut Satriani can't be classed as a blues musician. He is first, and foremost, a rock guitarist (one of the finest in my humble reckoning). If he does trample on blues territory sometimes, that would be understandable as many a rock artist is inspired by the blues.
from a narrow definition of blues, then definitely yes, i would agree with you. but if you read broadly about blues and its influences (and as you stated), then satriani would fall into the blues rock category. recently was reading up on blues and was astonished to see that most rock bands come under or have roots with blues music. wouldnt necessarily agree with it and i would lean more to the narrower definition of blues music
with satriani its the blues influences that i like, and perhaps thats why i've pegged him as a blues guitarist in my mind. but again, i stand corrected like you said, he;s not a blues guitarist in the purist sense