Well, the carbon in the nanotube will not react with the COOH. Carbon in a nanotube already has four bonds, in a graphite-sheet like structure. You will not be able to form a bond between that type of carbon atom and your acid. If there was any way to do that, it would form the bond on the outside of the tube (due to relieving the stress of the curved structure) or at the very end of the tube (where some of the carbons do not already have four bonds to other carbons), not inside.
You can, however, get the molecule containing the acid inside the tube. That would be a very hydrophobic site, and it would probably actually be two carboxylic acid molecules held head-to-head by hydrogen bonding between the carboxylic acid groups, but if the rest of the molecule was long straight alkyl chains, it could probably be done.