<p>Yes it would, which is the advantage of going to UIUC versus U. of Toledo, for example. However, as long as you go to a school that is known at least regionally as a quality engineering school, you can get a good enough job to get that same high quality second job as long as you are a good enough candidate and work to show that. It is harder to do and may take a little longer, but you still can eventually have that opportunity. However, going to the #25 ranked school for your undergrad is not going to be a huge difference from going to #12 or something like that. Both would most likely have plenty of recruiters from around the country. The only time that school prestige matters significantly is for grad school apps or if you want to get into something like ibanking. Otherwise, with the right amount of work and planning, you can make up for many of the disadvantages of going to a less known school.</p>
<p>If you have the opportunity to go to a top school, then by all means do, because they will have MORE of the top companies there so you will have a little better selection, but it is not the end of the world if you go somewhere that is a little less known. Far from it…</p>