No. In fact as I understand it, black holes make things even worse. Suppose you dropped a TV set into a black hole. The entropy of a TV set is very small because it is a highly-ordered piece of matter. It falls into a black hole and becomes unavailable to the rest of the universe, which means that the universe has lost some order ( information) that it originally contained. But, if you wait something like 10^60 years, the black hole will gradually evaporate into a cloud of subatomic particles, mostly electrons, positrons, neutrinos and some heavier particles. But these particles will carry no information with them about the particles that originally constituted the TV set that went into the black hole in the first place; the black hole doesn't even return one electron or one proton for everyone it has absorbed! Not only is the black hole increasing the entropy of the universe, but it is doing so in the most thorough of all possible ways by not even preserving the number of particles that went into it. All it preserves is the total mass/energy equivalent.
To my knowledge, black holes increase the entropy of the universe by evaporating via the Hawking mechanism. Were this not the case, there could indeed be some problems thermodynamically. But I am not any expert on these matters; just a spectator!