Yes, it was used for the services to Timperley-Lymm-Warrington BQLL-Ditton-Liverpool services before they were withdrawn in 1963.
Oxford Road was rebuilt around 1960 as a terminus for the WCML AC electrification from Crewe, with the Altrincham DC trains terminating in the bays.
Before that the Manchester-Altrincham DC electrification ran from Piccadilly (London Road), and it was only in 1960 that MCO became an interchange station from the east.
Going even further back, the CLC system trains also used Oxford Road before Manchester Central opened, so they would also have used the bay platforms.
The CLC remnants (to Liverpool and Chester via Cornbrook) came back in 1969 when Central closed.
Oxford Road lost most of its need for bays when the Altrincham line was converted to AC and trains ran through from Crewe/Wilmslow.
Chester trains later ran directly into Piccadilly via Stockport when the direct route via Sale was converted to Metrolink.
The sole survivor of all this is the CLC Liverpool stopper.
It is also very handy during disruption though, with ATW South Wales services frequently diverting via Warrington BQ into Oxford Road.
It appears the new service from Bradford via the Ordsall Chord will terminate in the MCO bay initially.
https://en.wikipedia.org/wiki/Manchester_Oxford_Road_railway_station