Probably not xd
I would assume that Jiraiya doesn't get all the benefits, such as sensing danger, etc. because he is not in perfect sage mode.
Evidence that supports this is when the Paths of Pain snuck up on him, which shouldn't be possible if he can sense both chakra (Naruto could sense all the chakra signatures in Konoha), and danger.
So I would guess that Jiraiya has a lesser boost to strength and speed, and doesn't get the sensing bonuses, as he is not in tune with nature.
I just reread that chapter, so I guess you are right about the sensing thing
I don't know if I agree on a lesser boost of strength and speed though
he most likely does get a lower boost in speed and strength but his base speed and strength is probably higher than naruto's so it doesn't make a deference