i can speak to this since i worked closely with a nurse recruiter at one large teaching hospital when i was a nurse manager and a member of the new grad orientation committee. in general, the answer to your question is no.
however, the smarter recruiters who know their area know more about the area nursing schools than you can imagine. they keep contacts with the instructors and program directors at the schools as well as with managers and recruiters at other hospitals. many of your clinical instructors are/or were staff nurses at local hospitals and it is highly likely that one of the nurse recruiters you end up talking to knows one or two of your clinical instructors through a work situation. so, i have written about this a number of times and it is based on my experience working as a nurse manager hiring new grads and working with human resource people and nurse recruiters.
treat nursing school as if it were your job. i can't shout this loud enough. you are being evaluated and assessed in your performance every single day just as any employee at a job. your instructors and professors are compiling written data on each of their students. some of this data goes into a permanent file that is used in later years to help other nursing department instructors in later years who may not even know you provide information for job references for you. if you think i'm making this up, ask about this. despite strict rules on what can go into files, stray sticky notes get left in files all the time.
your first job references must come from your nursing school instructors. therefore, it is imperative that you have made a good impression. can your instructors say you were interested in nursing? did you whine and complain about all your assignments? were you always the last one in line to perform your return lab demonstrations? when volunteers were asked for, did you suddenly disappear? did you show eagerness to learn or need a whip to keep you going? did you accept mistakes you made like a man/woman, own up to them and demonstrate integrity in correcting and improving your practice? did you cut classes? were you a troublemaker? your instructors are going to be asked about your personality and character. make no mistake about the fact that employers are looking for people who are going to make good employees as well as deliver the goods as nurses and your grades don't show that. did you stumble through new procedures saying "glad that's over"? or, did you ask for more opportunities to practice and hone that new skill? no one wants a problem employee and i can tell you that as a nurse manager i want to try to elicit that potential information before i hire someone and have to deal with a bunch of behavior problems and bad attitude headaches.
it's not only what is written on a reference, but what is not written that gets considered. a potential employer of a professional person (and that's what an rn is) wants to see things about you like this: positive attitude, has a pleasant personality, communicates well, energetic, not afraid to step up and be responsible, respectful of others, able to work with minimal supervision, flexible and adapts to change readily, is a team player, has the ability to be an effective leader, can tolerate stress, has good problem solving skills, always eager to learn more and was a good learner in school. if some of those things are not on the paper i've got to go "hummm?"
the good ol' boy network still exists. even though you might have listed the two nursing instructors you wanted to give your references, our recruiter still picked up the phone and called the school to talk to the instructors she knew and whose opinions she had learned to trust in the past. no, it's not legal anymore, but who is going to tell and how are you going to prove it?
i cringe every time i see a post from a student either intimately involved in a hot issue or considering getting involved in one that is going on at the nursing school with the dean or the nursing instructors. employers get wind of that stuff too and more likely than not it's not good gossip that they hear. most employers aren't likely to hire people who come with baggage like that.
just remember that all your actions have consequences. the people in charge in the working world are more conservative than you might want to think. ultimately, those are the people you have to impress. so, c's are good. your instructors are right. just worry about passing your classes, passing the nclex and demonstrating that you have the right stuff to be an rn and work in the world as an rn.