Is it possible to use Thunderbolt networking and regular ethernet networking simultaneously? I'm considering purchasing a new iMac and recently learned that Thunderbolt 3 can be used to create a Thunderbolt network bridge between two Macs.  I assume that connection over Thunderbolt will be many times faster than an ethernet connection.  

I also want both iMac's to be connected to my LAN via their ethernet adapters.  Is it possible for both of these connections to run independently, simultaneously, so that each Mac can still "talk" to the internet and other devices on the LAN, but "talk" to each other at Thunderbolt speeds?
Yes, that is definitely possible - indeed this is what happens if you hook them up like this.

Thunderbolt 3 enables transfer rates up to a theoretically high of 40 Gbps.

The relative speed depends on the type of Ethernet connection you're comparing it with. If you're using 10-gigabit ethernet - then you're probably not going to see any practical benefit from the Thunderbolt 3 connection (if you're not transferring stuff from disk, you might get huge benefits though). If you're using gigabit or slow ethernet, you're going to see a massive improvement in transfer speeds.