Do nucleophiles add to carbonyl carbons?
Yes, the many of the reactions of carbonyl compounds involve nucleophilic attack at the carbonyl carbon.
The carbonyl carbon has a partial positive charge, so it is a perfect target for attack by a nucleophile.
Some reactions that involve the addition of a nucleophile to a carbonyl carbon are:
Reduction by LiAlH₄
Formation of cyanohydrins
Hydrolysis of esters
Formation of esters from acid chlorides
Conversion of esters to amides
Here's a video about nucleophilic addition to carbonyl compounds.