Can voltage decrease when current is increased?

Yes and no. Voltage is directly proportional to current from Ohm's Law (V=IR.) Thus, when voltage increases, so does current.

However, voltage can be inversely proportional to current in some situations. This can be seen in a transformer, where current and voltage are inversely proportional due to the law of conservation of energy, in which P(in) must equal P(out). Thus, a greater input voltage leads to a small output current.