Hi Anthony - welcome to the forum!
I haven’t used mediafast for a while, in the latest firmware you can use it for local content storage and as a hypervisor to run virtual appliances.
To cache user requested content, the mediafast has to sit inline from a SSL perspective and act as a SSL proxy between the LAN clients and the internet. To do this you would need to add its certificates to each device that will access the internet via the medifast (which works fine in a enterprise / educational environment where you have device management in place).
Let’s see what responses you get (and lets ask @sitloongs for his input too) but I don’t think the product will work like you need it to unless you have full LAN device management in place.
What’s the application / use case?