Is it possible to be pregnant, and have the implanon, but still get a period?

Possible, not likely: Implanon is not 100% effective in preventing pregnancy, so you could be pregnant. As far as a period, it would not be expected during pregnancy, but first trimester bleeding can be misinterpreted as a period in such cases. Check a home pregnancy test asap and see your gynecologist to find out what is going on. Take Folic Acid 1-5 mg daily and best of luck!