Does valacyclovir affect the combination birth control pill?

No. Valacyclovir is an antiviral drug, not an antibiotic (there are major differences), and only antibiotics are said to interfere with hormonal contraceptives. But even the antibiotic problem is seriously overblown; it's not quite an urban myth, but it's close. Very few antibiotics, and only in giant doses. Oral antibiotics virtually never interfere; you really needn't be at all worried about it.