Is there a way to sync music between a PowerPC Mac and an iOS 7 device?
Solution 1:
There are many apps that can move data on and off an iDevice, albeit not in the same "sync" model that iTunes uses. Try the trial of iExplorer, for example.
Solution 2:
Yes - multiple third party products allow Mac to write directly to iOS devices including PhoneView.
Their requirements page lists 10.5 Mac and iOS 7 support for version 2.9.4 of the product.