Can hiring managers see how long you have worked at previous jobs? and should I put a short term job on my resume?

Hi all, currently I am working at a restaurant but I am planning to resign after being there for just over a month. The general manager / restaurant owner and I are on reasonable terms and we agreed that I will work for the duration of the winter break. I am worried that if I worked there for just a month, it may look bad on my resume and work history.

I have heard from my high school advisor that if I worked for just a month at someplace I should not put it on a resume, but another advisor told me that the future employer can see that I have worked at that place and if its not on the resume then it makes me look dishonest.

I am curious to know if my one month long winter break job can look bad on my resume and if any future employer can see how long I stuck around at my previous jobs?

PS I did provide my SSN to the employer so its not cash based and he wont settle for cash payment anyways. Also, I do understand that most employers are not likely to be willing to hire people who just keep hopping from job to job as it shows the applicant is not likely to be reliable.

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