Is a virgin pregnancy really possible?

No: Not unless you have have in vitro fertilization (IVF) performed.

Not that we know of: Biologically there has never been a documented case of "virgin" pregnancy in humans - so called parthenogenesis. It does occur in other species. But presently it could occur in the setting of various forms of "artifical" insemination - as in sperm being deposited into the vagina/uterus without penile penetration. Of course, depending on your religious background you may feel different.