No. The way the rules are worded, if a person can be claimed by someone else, they can't claim a dependent of their own.
Your GF can be claimed by you if all the following are true:
- she lived in your home the entire year
- she has less than $4200 of taxable income
- you paid more than half her support.
In any case, if her taxable income is less than $4200, her total child tax credit won't be $2000, more like $300, because her earned income is too low to qualify for much of the "Additional child tax credit."
