Am I allowed to enroll in a dependent care flexible spend account even if I won't have a dependent to claim on my tax return for that year?

You can only use the FSA for 2017 if you will have physical custody more than half the year (183 or more nights).  Even if you waive the dependent exemption and child tax credit per the custody agreement, you can still use the FSA as long as you are the parent with custody more than half the year.

On the other hand, if you have custody less than half the year, you can't use the FSA even if the custodial parent gives you the release form for the dependent exemption and child tax credit.

If you are waiving the dependent to the non custodial parent then you are still allowed to take the child care credit and thus may use the FSA option at work. 

If you are unmarried or never married and live apart and share custody, then:

The parent with whom the child lives more than half the year (184 or more 184 nights for 2016) is automatically entitled to claim the child as a dependent. This is the custodial parent. (IRS determines custody based on where the child lives, not any court order or agreement.)  The non-custodial parent is not entitled to claim anything.

However, the custodial parent can sign a release (form 8332) allowing the non-custodial parent to claim the child as a dependent.  You can download this form from the IRS web site.  The custodial parent signs it and gives it to the non-custodial parent and the non-custodial parent mails it to the IRS after e-filing the rest of their tax return.  In this case, the non-custodial parent can claim the dependent exemption and the child tax credit.  The non-custodial parent can never claim earned income credit, the dependent care credit (day care credit) or use the child to qualify for head of household status.  Those benefits always stay with the custodial parent.