The answer is YES. Charged particles indeed attract uncharged ones.

This is due to the phenomenon of "Charging by Induction". When a charged body(say negatively charged) is brought near an uncharged one, it induces an opposite charge(positive) on it and hence attracts it towards itself. This can be explained as follows :-

The negatively charged body can be thought to be an electron rich specie. When brought near the uncharged body, it repels the free electrons from the uncharged body towards its farther end. As such, the closer end of the uncharged body now experiences lack of electrons, which is a characteristic of positive charge. Hence, the ends of the two bodies develop opposite charges and mutual attraction occurs.

The same theory applies for a positively charged body which can attract an uncharged one.