There is a lot of confusion about Miranda warnings and the role they play in an arrest. Generally, law enforcement officers are required to read a person in custody the Miranda warnings before questioning him. If they fail to do so and there is no relevant exception to the requirement, then any evidence gathered during the questioning may generally be suppressed (kept out of court). That generally doesn't mean that charges have to be dropped, only that evidence collected illegally can't be used. You may find the link below helpful; the page explains Miranda rights and the consequences of failure to read those rights in more detail.
The short answer is generally, NO. Miranda warnings must be given before custodial interrogation begins. There are many subtle issues that can impact the application of this rule; and, whether a subsequent statement will be suppressed. A dismissal is an extraordinary remedy that a Court is unlikely to impose, unless it is clearly established that the only State evidence was a tainted statement which resulted from a direct violation of your constitutional rights. Discuss this in person with a criminal defense lawyer admitted to practice law in the State where the charges are pending. Good luck.
This answer does not, nor is it intended to, create an attorney-client relationship; or, constitute either legal advice or attorney advertising. Rather, given the nature of this forum, it is offered solely for information purposes, as a starting point for you to use when speaking directly to a lawyer in your State. Do not assume that the legal conclusions I mention that pertain to NJ are applicable in your State. Since the facts of each case are different, it is critical for you to consult with qualified counsel with whom information can be shared and assessed under an attorney-client privilege, so that competent advice can be obtained on which you can make informed decisions. Contact an experienced criminal defense lawyer admitted to practice in your State before making any decisions about your case.