yes it is possible to become pregnant and have a heavy enough bleed to look like a period and not pregnancy.

Here is something I put together from my first pregnancy

I could remember that year because I was 16, and remember thinking for Christmas I was in the clear. I can remember December 20th puking my dinner up, only cause I remember my friend joking that I was pregnant. So when i got my period i was so excited.

Later did I know that I would miss my period in January, tested january 30. Only cause I slept for a week straight and my mom made me get a test. IT WAS POSITIVE. February 25th I found out I was pregnant.

Later went for another sonogram

which put me at conception being

Finally two weeks early and a c section (cause she was breech)

5lb 3oz 17 inches long

She is now almost 10

Well that's my story, of how I became pregnant before my "period" (probably heavy implantation bleeding).