It will probably show up, but doubtful it will be a problem for you. You were DETAINED not ARRESTED if no case was ever filed.
The opinions rendered herein are based on general principles of law. Laws vary from jurisdiction to jurisdiction and there are often numerous factors which can render advice or an opinion inapplicable. You should NOT make any decisions about the handling of a legal matter without first directly consulting with an attorney about the particulars of your case.
You were booked, so your identifying information was uploaded into the DOJ database that Livescan accesses. My anecdotal information from clients suggests, for you, that this run in with police will appear on Livescan. There will be no court case associated with this, but it will appear.
Having the record sealed does not bar Livescan from reporting anything. Sealing a record just means that if there were a case, no one could look at the case documents without permission from a judge.
What I would do if I were you is look into filing a petition for factual innocence to have the record of the detention destroyed so it is removed from the DOJ database and then Livescan cannot report it or see it either. Under 851.8 of the Penal Code, one may ask for a finding of factual innocence. This forum is perhaps not the best place to give you the full explanation of how it works. My website has a little article on it that you can read and understand how long it takes and how hard it is to get.
Good luck with your career and keep taking all the college level courses you can.
The arrest will probably be on there. I think that if you are upfront about it and tell them the circumstances, or even just attach what you wrote above, you will be fine.