I think the service road should be routable for cyclists; taking a longer road-based detour in this area if the route would otherwise follow this small segment of road wouldn't necessarily be a good idea for cyclists.  However, the barrier (a lift gate, if I remember correctly) itself should perhaps be mapped as bicycle=dismount to indicate that you can't cycle through it but can easily dismount and push a bicycle around it.  Ref: https://wiki.openstreetmap.org/wiki/Tag:barrier%3Dlift_gate