A case with unemployment has nothing to do with a wrongful termination. What happens is that you file a claim for unemployment insurance benefits after you are terminated. Answer to "can I be terminated....?" is of course, yes, you can, legally be terminated for almost anything or in any way. The company doesn't even have to follow its own regulations or company handbook. Only if the termination is because you are a member of a protected group according to EEOC, or something very specific like that is it a wrongful termination, though you may think they did you wrong.
But you file for unemployment, detailing exactly what happened during your termination, as in what warnings you received, what you were told, what exactly went on, and then they will determine first if you have monetary eligibility, which means you have worked for covered employers in the last five quarters enough to set up a claim. Then they'll contact the employer and get their exact story on the reason why you were terminated. They may call either of you in or talk to you by phone to obtain more information, but within a couple of weeks they will make an initial decision whether to approve or deny benefits. Both parties will be notified and will be given an opportunity to appeal the decision. Then a hearing will be held, with you and the employer both present, either in person or by telephone. This will give a second decision to either approve or deny benefits.
You will be asked about the exact circumstances under which you received your warning which if I understand it correctly, then turned into a firing. Did you know that cell phone use was forbidden? What was the company's policy (in your understanding) about cell phone usage? Had you ever had any prior warnings? They'll ask all these types of things, and then they'll ask the employer all about it. They may decide that the company did not follow their policies, and therefore gave you no opportunity to change your behavior and not be terminated. It all depends. But whether they approve benefits or deny benefits, it has nothing to do with whether or not your firing was legal or wrongful. In an at will state, almost every firing is legal. But the downside for the employer is that if you are terminated and they cannot show they had a valid misconduct reason, you may be approved for benefits, and that will cost them money in unemployment rates.
