About 4 Weeks Ago, I Started A Birth Control Pill

About 4 weeks ago, I started a birth control pill called reclipsen. My period is late and I have no idea if I will miss it or not and I did not have any sexual encounters. Is it common to miss your period while in this pill?
Also, let's say I did have a sexual encounter but my period was late or didn't come on the pill. Is there a possibility in this scenario that I could be pregnant?