No, if the hydrogen atom's energy were proportional to n (or any power of n), it would become infinite as n increased in size. However, n2 has an inverse relationship with the atom's energy. As a result, as n increases to infinity, the atom's energy gets closer to the ionization energy, or 13.6 eV, which is a value that is a finite amount above the ground state. Its energy loss is never greater than the ionization energy as the electron transitions from one bound state to another. Any emitted photon has a limited amount of energy and frequency.
As n rises, energy magnitude decreases, but the electron's energy rises because of the negative sign.
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