That is correct. Lee cared for his men. If the number of men in each army had been comparable, Lee WOULD have won.
No, Lee would have lost. You said it yourself, you didn't think that he would have done what it took to win.
And for the record, when you look at casualties as a percentage of the forces under his command Lee's butcher bill throughout the war was consistently higher than Grant's.
I believe "IF" is the Losers' Anthem.