Every case I've seen suggests that the answer is yes.
Most on point is N.C. v. Com., 396 S.W.3d 852 (Ky. 2013), dealing specifically with whether an SRO was permitted to question a student without advising him of his rights to remain silent and have an attorney present:
If he had been an adult under these same circumstances, there is no question that the statements would not have been admissible under Miranda. It also is apparent that the above-noted procedural requirements in place in the UJC would require the equivalent of Miranda warnings before the court could take testimony from a child. The clear intent of the statutory proceedings is to ensure that a child is not led to unknowingly incriminate himself. It makes no sense that the safeguards required of the court should not apply to the evidence offered against the child. Such an end run would defeat all precepts of due process.
An Indiana court reached the same conclusion in D. Z. v. State, No. 32A05-1708-JV-1907, 2018 WL 1004463 (Ind. Ct. App. Feb. 22, 2018):
Turning to the facts before us, we conclude that D.Z. was submitted to a custodial interrogation at which he should have been advised of his rights pursuant to Miranda. The evidence establishes that after Dowler and Officer Flynn's investigation was complete and a suspect was identified, Dowler called D.Z. to his office for a discussion. The assistant principal questioned D.Z. in his office with the door closed. No reasonable student would have believed that he was at liberty to leave the office—it is undeniable that juveniles are susceptible to the influence of authority figures and the constraining effect of being in a controlled setting of a school, where “disobedience [can be] cause for disciplinary action.”
These are cases asking whether students need to be Mirandized, which assumes that the students have Fifth and Sixth Amendment rights of which they need to be advised. But keep in mind that the duty to Mirandize only arises in the setting of a "custodial interrogation," which is a notoriously slippery standard. Of course, the fact that you don't need to be Mirandized doesn't mean that you don't have those rights.
Minors have clearly had Fifth and Sixth Amendment rights for 50+ years. From Application of Gault, 387 U.S. 1 (1967):
We conclude that the constitutional privilege against self-incrimination is applicable in the case of juveniles as it is with respect to adults.
[W]e hold now that [the assistance of counsel] is equally essential for the determination of delinquency.
Moreover, I would expect the student to have a First Amendment right not to speak to a police officer. That was the holding in In re Juan A., 179 Cal.Rptr.3d 235, 241 (2014), a North Carolina court in a case dealing with a student who refused to answer an SRO's questions about a fight at school:
[W]e do not believe that mere expression of a desire not to talk with police is criminal. The officer here certainly had reasonable suspicion which would support a detention. Had she attempted to detain the Minor, his resistance could justify a true finding. In this case, however, the Minor yielded immediately upon police demand. That he did not want to talk to the officer before that point was not a criminal act.