Not possible. The path is hardcoded into the program. It is not a setting in the .ini or the registry.
What you CAN do however is to store your 'favorites' as SQL on any mapped (network) drive and use the 'file:// ..' option on the individual machines linking to the folder containing the scripts themselves.
You will need to create only one local 'favorites' folder and distribute to all machines. But the network drive must be mapped to the same drive letter on all machines.
And this way you can of course have both 'shared favorites' and 'personal favorites'