Can a girl pop her cherry if a guy fingers her?

Well, let's rephrase that question in terms that are respectful towards people.

Can a girl's hymen break during manual sex?

Yes, the hymen can be torn during manual sex. If somebody inserts fingers into your vagina, and you still have some hymen tissue there, the hymen can tear if stretched too much. A lot of things can make a hymen tear. Tampon use, vigorous exercise and pelvic exams (though doctors try to be very accommodating to avoid this) are some non-sexual ways to break the hymen.

In case you weren't sure where the hymen was, it's a thin membrane that starts out by covering the opening of the vagina. Many women don't have a hymen by the time they become sexually active. The hymen usually wears away as a woman grows up. If it didn't, how would our menses leave the body? Some women will have remnants of hymen tissue at least partially covering the vagina, and this is what can tear during sexual activity.

Many girls wonder about how their hymen related to being a virgin. If this is a concern for you, please read Magical Cups & Bloody Brides: Virginity in Context and 20 Questions About Virginity: Scarleteen Interviews Hanne Blank.

If you want to know about the hymen and the rest of your sexual anatomy, check out Pink Parts - Female Sexual Anatomy.