The plan document should specify the beneficiary if there is no designated beneficiary. The plan document must be followed.
So, no to your question.
If the plan provides that, in the absence of a designated beneficiary, the eldest child of the participant is the beneficiary, and said daughter is the only child of the participant, then the daughter is the beneficiary, but not a designated beneficiary.
I doubt that the plan provides that the eldest child of the participant as the default beneficiary. The plan might provide that the children of the participant are beneficiaries, and equal shares.
The plan might provide that the estate of the participant is the beneficiary. If the daughter is the administrator of the estate, then the daughter will manage the plan benefit.