I spoke with the CX Service Manager at the Service Desk. Which flights are you on? There are four flights a day: early morning, mid-morning, afternoon and night time.
The manager indicated that, for example if you were trying to check-in for the night time flight in the morning, that would not be possible. It seems the main issue is that the Ground Handling Agent for CX doesn't like getting bags for later flights as they then have to have a make-up area for that flight, which may not be possible given how busy it can get in the baggage handling area. (Slight chance the bag may get misplaced as well).
However, while it is not ideal, they did admit that it may be possible to drop bags for the afternoon (3:40pm) flight during the check-in time for the 11:30am flight.
Check-in counters are not staffed at all times. E.g. After check-in for the 11:30am flight, they close down and then re-open again 3 hours prior to the 3:40pm flight.
Doesn't sound like there's any guarantees, but you may get away with it, and maybe even more so if you are OWE. As a suggestion, perhaps if you can't convince them to let you drop your bags off, and you have to end up hanging around landside until you can, then perhaps you could convince them to give your Mum an entry pass to the Lounge.
