No. Virginity is most often refered to as the absence of penetration of the penis into the vagina or rectum. Although a tampon may break the tissue that partially blocks the vaginal opening, it does not cause a loss of virginity.
No; still a virgin! For a woman or girl to lose her virginity means that somebody's penis has gone into the opening of her vagina. A tampon, vaginal speculum (used to look at the cervix), ultrasound scanning probe, vaginal suppository medication, somebody's finger, a foreign object, a toy, etc... Can all go in and out of a woman's vagina and she will still be virgin. Also, there is no such thing as a virginity check.