Any convergent sequence of real numbers will converge to a real number.
If we look at the question directly as asked, then the answer is yes, as the real numbers are a subset of the complex numbers. Then, any convergent sequence of reals will converge to a complex number.
Assuming, however, that the question is asking whether there can be a sequence of real numbers which converge to a number with an imaginary component, the answer is no.
This shows directly that given any proposed limit with an imaginary component, we can demonstrate that the sequence does not converge to that limit by setting