Does the college you go to for mechanical engineering affect you in future job employment?

You should only consider colleges with an ABET accreditation. Most companies seek out college graduates from universities with an ABET accredited degree. Furthermore, it is a lot more difficult to get licensed without an ABET accreditation degree.

Yes!

To continue, I think we need to define what a university is compared to a school, in terms of higher education. This should help provide a better understanding for the remaining of my post.

A "university" is a group of schools for studies after secondary school. At least one of these schools is a college where students receive a bachelor's degree.

One thing to consider, just because the university is the best, does not mean that the engineering school or specific engineering school shares the same ranking. For example, I went to a top 100 US university, but they were ranked number 1 in the nation for their school of journalism." - https://www.studyusa.com/en/a/107/what-is-the-difference-between-a-school-college-and-university-in-the-usa

So to answer your question, search for the best school of engineering (I would even narrow the search down to what field of engineering) you can get into, or a school of engineering you want to target (depending on your current academic year.) But don't freight if you are not accepted to the best school in the world. There are plenty of successful engineers from all different educational backgrounds, just try your best!

Only for your first job.

As my esteemed colleagues have noted, a degree from an ABET accredited program is important, but it's also important to know how many engineers graduate each year compared to the number of incoming freshman, how many graduate in 4 years, how many get jobs within 6 moths after graduation, placement rate for internships and co-ops.

Finally, student debt is a huge concern. Please do not take on more than one year's salary in debt -- so no more than $15k a year or $7.5k a semester (starting salaries vary depending on disciple and location, $60k is a reasonable expectation). There are plenty of schools out there that offer quality engineering programs without crazy high price tags.

Once you've landed your first job, the rest is up to you. Alumni networks are helpful, but your hard work and success as an engineer is up to you.

Yes. Good colleges makes good professional people, but you need to be dedicated, the college isn't a warranty that you will reach your goals, you must focus and learn all you can and never stop studying. Keep always improving your knowledge.

Yes. Besides being ABET accredited, the more prestigious employers do recruiting at the better ranked schools. I have known many engineers who are very talented who went to lesser known schools. However, as a rule the top schools get the more motivated students who become the more motivated engineer.

Short answer, if you are talented and prove yourself, you will have a great career. If there are reasons that you cannot go to a highly rated school, but still apply yourself, you will do well. After you have some experience, the school matters less that what you have done in your career is what you will be judged on.