Absolutely! According to Bandura and his theory on modeling, children would be affected by other children in the daycare and their actions. Young children are especially susceptable to picking up new habits or copying actions/words they are hearing and seeing. Children in daycare may also be more sociable and know how to better develop relationships with others. Of course, having environmental influences from the daycare does not mean a child will turn out in a certain way. There are several other influences (ie home, genes, etc.) that can affect children.
Good luck on your paper!