Yes they do. One of the major reasons people use matrices is to maintain or promote differentiation. Years ago attachment was thought of as simply that...now we know attachment proteins in a cell contacting the proper matrix is a survival signal and a differentiation signal. Many of the different attachment proteins in a cell act as signal transducers that alter gene expression pathways in a cell. This is one reason why you read so much about 3D culture. Most cells do not live in 2D but in 3D and allowing them to grow in a more natural way causes cells to do things in 3D that they can not do in 2D. I often do experiments with a pheochromocytoma cell line that will differentiate into neuronal like cells if plated on a positive charged dish.