Caro-Kann Defence against 1.d4

Totally fine, but a 1.d4 player will only play 2.e4 if he plays Caro-Kann himself or if he is a 1.e4 player by birth. And if White will play Nf3 then c6 isn't Black's most active choice. But 2.Bf4 Qb6 may be a way to confuse things!

There is nothing "wrong" with the move, but you have to realize all possible benefits AND consequences (to me, the biggest issue would be #4):

1) Do you play BOTH the Slav AND the Caro-Kann (Your post implies Yes)

2) What do you prefer to do against the London and Jobava? If you would prefer a line that features BOTH ...d5 and ...c6, then it doesn't matter which you play first. If what you would do against the London doesn't involve either ...d5 or ...c6, I would suggest not playing that move first, like if you prefer ...d5, ...e6, and ...Nf6 against the London and the Jobava, then 1...c6 is not a good idea. If you would play ...c6 anyway against the London, doing 1...c6 first is no issue. Keep in mind, after 1.d4 and 2.Bf4, both the Jobava (3.Nc3) and the London (lines where the Knight goes to d2 instead) are possible.

3) One benefit to 1...c6 over 1...d5 is it makes 2.Bg5 bad. It doesn't lose White a Bishop because he has not played e3, but 2...Qa5+ forces either the allowance of a Queen trade with 3.Qd2 or a waste of time with the Bishop with 3.Bd2.

4) Would you play ...c6 against e3-lines with the Bishop left behind the pawn chain. The Colle System is not scary as the Anti-Colle Lines where the Bishop comes out to f5 or g4 virtually force a Slav. But what about the Stonewall setups? 1.d4 c6 2.e3 intending 3.f4, do you really want to play ...c6? Or would you rather play ...c5? That would be one reason to play 1...d5 instead of 1...c6.

5) Are you ok with a Slav setup against 2.Nf3 lines?