It is possible, but the answer depends on why you were gate-locked at the prison and whether that information has been shared with the county jail.
Gate locking at a state or federal facility creates a record within that institution's system. County jails operate their own separate visitor approval processes and do not always have access to or share information with the state prison system. If the county jail runs its own independent background check and your denial at the prison was not flagged in a shared database, you may be able to get through the county's vetting process without the gate lock affecting it.
The risk is that some jurisdictions do share visitor-restriction information among facilities, particularly within the same state system. If the reason for your gate lock at the prison is recorded in a way that a county jail background check would surface, the denial could follow you there as well.
The safest approach before attempting a visit is to call the county jail and ask about their visitor application process without disclosing the prison gate lock situation. Go through their standard application, submit to their background check, and see what comes back. If they approve you independently, the visit is legitimate on their end.
If you get denied at the county level as well, it indicates the restriction is being shared across systems. At that point the only path forward is addressing the underlying reason for the gate lock at the prison through the warden's office or with legal assistance.
In the meantime, letters through InmateAid keep communication open regardless of visitation status.