I believe that you can. Liking someone is superficial, totally surface, but love is deeper. Love allows you to look beyond certain qualities, but like is fickle it changes quickly and easily. I think we like things in spurts, it comes and goes.
It's like being a parent, your child will go through phases where you won't "like" his/her personality, but the fact that you love them never changes. Romantic relationships are similar, because your partner will also go through phases and during those times he/she may not be likable at all, but the love can remain.
You just have to remember that loving someone is not always enough and vice versa.