Yes it could.
Don't disturb the material while it is dry. Airborne asbestos fibres are very hazardous. Don't keep the unit indoors.
If you soak the whole asbestos-containing works in a pail of water and keep it outdoors,wet, it will reduce risks considerably.
Look in yellow pages or google for your local asbestos abatement professionals – they will tell you how best to deal with it safely and for a small item like this, probably quite cheaply. They may just ask you to remove screws then bring it to their shop or an abatement site wet and in a sealed plastic bag, where their technicians will deal with it and give it back to you washed and cleaned of asbestos.
Glass wool or kaowool is a good replacement.
Good luck, be safe. JD