No, protons and electrons do not cancel each other out. Protons and electrons have opposite charges, but they do not have the same magnitude of charge. A proton has a positive charge of +1, while an electron has a negative charge of -1. This means that one proton and one electron do not cancel each other out completely. Instead, they create a net charge of zero.
In an atom, the number of protons and electrons is equal. This means that the overall charge of an atom is zero. However, if an atom loses or gains electrons, it can become charged. A positively charged atom is called a cation, while a negatively charged atom is called an anion.