The lower the dose of the pill, the more important it is to take it at the same time, I think, but I'm not a pharmacist.
I've been on the pill for a total of 25+ years and they've always been effective, and I don't take them within an hour each day, just always at the same general time (morning or evening) each day. I can't take low dose pills, though, as I have too many side effects, like breakthrough bleeding, with them.
When I first started the pill at age 20, the doctor told me they were effective "immediately". Now doctors do tell you to wait at least one month for them to be effective.
And most antibiotics do NOT make the BC pill ineffective. That's been disproven by many recent studies.