Yes. She can claim the children even if the Dependent Care FSA is reported on your W2. The disadvantage of this is that neither parent would be able to claim the child care dependent credit if you file married filing separate in accordance to Topic 602 of the IRS.
One note of caution, the rules say that if you file separate, each spouse is only allowed to deposit $2500 in their account. If you file married filing jointly, it is $5000. Since you deposited $3300, the $800 will be taxable income to you if you file separately. If you file MFJ, the $3300 is less than $5000 thus you will not be taxed for excess amounts.
My suggestion is to file married filing jointly unless that EIC amount is too good to pass up. You may end up paying more out of your return than you may expect thus may not be worth the trouble for the added bit of money your wife's return may generate.
Child and Dependent Care Credit & flexible benefit plans
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