at the university i work for applicants are actively discouraged from calling. there is also no single person responsible for hiring decisions. instead there is a formal set of protocols which somewhat resemble the process of peer review, but instead apply to finding future colleagues. there is a search committee, comprised of full-time faculty, one of whom acts as the search committee chair. the main job of the search chair is to facilitate meetings between the faculty in the search committee and act as liaison between HR and the department chair, program head, or school dean. all faculty members on the committee including the chair have equal input and weight.
though i'm not sure what goes on at the community college level or by individual institution, this is how they typically do it at universities, at least the big ones, or the legit ones.
you will either make the cut with your qualifications or you won't. applications don't frequently get too lost in the shuffle, as they are concurrently reviewed by multiple faculty members (between 8-10 where i work) who then share their evaluations of each applicant. this takes place in meetings where each applicant and their suitability is reviewed and discussed. and yes, sometimes searches, especially in universities located in new york city, receive enormous numbers of submissions (in the hundreds.)
your best bet is to really do your research. what is the student profile of the program or department you are applying for? what do they see as their "market" or mission? if you lack teaching experience, how can you highlight experiences in your professional life which may have prepared you to become a great teacher? do you bring skills, contacts, or something unique to the program? do you have an articulated philosophy about learning and education? VERY IMPORTANT: can you talk about your vision for your field beyond just a list of clients you've worked for or jobs you've held? that's why i suggested speaking with current faculty about their program or department. you can get a sense of what they're looking for.
as for having someone vouch for you, it only really works in borderline cases, where the applicant may have a lot of "real world" experience, but scant academic experience, or vice versa. in those cases someone's application might get through an initial round, but... in search committees there are SEVERAL rounds of elimination before finalists are selected. and... you can circumvent this process by anticipating what will be on the minds of the search committee reviewing your application and address it in the cover letter!!!
anyway, good luck again!