In my experience, yes, the college you attend can influence your prospects in the job market.
First, it is important that you select a school that is properly accredited or certified for your intended career field. Beyond this some schools vary with the quality and amount of career placement support offered post graduation. Alumni networks can also be great resources in opening doors and creating career opportunities after graduation. While some large schools have very active and far reaching national alumni network, there are many great schools that are smaller that offer great alumni resources, are very strong regionally or in specific industries.
Good for you for considering how the school you select will matter in the job market after graduation. it is a great question to consider when investigating which university to select.