By the book, sticking to the word of it, Combat Sense (the spell) gives no bonuses to the Astral Combat Pool (I think). But, after reading how Combat Sense works, would you allow it to give bonuses to the Astral Combat Pool?

Sphynx

Being as Astral movement isn't based on quickness but on intellegence, I don't think you'd be moving any faster...As for getting more combat...shoot, I dunno. AStral combat is always a little weird, kinda like Matrix combat. I think I wouldn't allow that...
If I were GMing I would think you woul dneed a seperate spell designed for astral combat...but my interpretation may or may not be cannonical.

I'd say it could be used if you had cast the spell while astrally perceiving, unless its a physical spell, in which case it doesn't because physical spells don't work in astral. I'd be inclined to say you could use it even if it is physical, because the IC description is almost like a sixth sense which I think fits equally well if not more so with astral space.