Yes, you can get between the DL gates and TBIT using the tunnels including the new airside T4-TBIT connector. It's actually a beautiful glass walkway. I think a couple of bloggers posted pictures of it when it first opened, so if you google "TBIT airside connector" or something similar you can probably find them.

In March, I had about a 9 hour layover in LAX. I landed on a DL flight in T6 and stayed airside to visit the T5 Skyclub and then the TBIT Star Alliance lounge. We then left the airport in an Uber to meet a friend.

When we came back, we ran into the only snafu in my plan. We tried to clear security at T4 because our DL-printed BPs for our VA flight showed PreCheck and TBIT doesn't have PreCheck. The contract line dragon at T4 insisted we couldn't clear security there because we were in the wrong terminal. I told him we'd used the connector that afternoon between T4 and TBIT but to no avail. I tried to find an actual TSA employee to whom I could appeal my case, but I didn't see any. We ended up walking back to TBIT for the long security line and the nude-o-scope.