Guessing there’s an omission in the sentence you quoted and that it is:
As-tu DROIT À un découvert (sur|avec|pour) ton compte courant?
You’re right it can be omitted (only in oral speech) and you can say:
As-tu un découvert sur ton compte courant ?
Which match the English translation you gave.
The “droit à” is implied because you’re asking if the person has the right to be overdrawn on an account.
Wordreference translation for “découvert” in the bank account sense is:
découvert nm (dette envers la banque) overdraft n
- J’ai demandé le droit à un découvert à mon banquier.
- I asked my bank manager for an overdraft.
So “an overdraft” literal translation is “droit à un découvert”, I assume because “découvert” ‘primary’ meaning is something not covered.
A variation to ask someone if he/she is overdrawn would use “être” as verb and would give:
Es tu à découvert sur ton compte courant ?
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