Absolutely not! The alcoholic residue is left unchanged.
General reactions for ester formation:
The reactions takes place between electrophilic carbonyl group of the acid, and the nucleophilic hydroxyl group of the alcohol. The alkyl residues on each species are along for the ride, and their integrity is maintained in the esterification reaction. Of course, the reaction spits out water, but the water derives from the groups attached to the ipso carbons.
The upshot of all this is that if I start with a primary alcohol, there will be a primary alkyl residue attached to the carboxyl, if a secondary alcohol, then a secondary residue.