Can an airline order a 777 with 787 flight deck avionics?
I'll answer based on the one precedent I'm aware of. Yes. But whether the manufacturer agrees is up to them.
In 1996 Saudia ordered 29 MD-90s with MD-11-style cockpits from Honeywell, including the overhead panel.
Which Honeywell then supplied for the MD-95 (later renamed Boeing 717) as well.
From Honeywell's press release:

Saudi Arabian Airlines (Saudia) has specified Honeywell's 8-by-8-inch flat panel liquid crystal displays for its new McDonnell Douglas MD-90 airliners.
(...)
In a separate development, Douglas has also decided to provide Honeywell's flat panel displays for the recently launched MD-95 aircraft program.

Regarding the specific 777/787 example, the 787 shares a lot already with the 777, which reduces the cost of training a 787 flight crew if they're already type-rated on the 777. Therefore, there's little incentive for both the airline and manufacturer to go that specific way.

For different reasons (not one airline's order) the 767-400ER comes with a 777-style cockpit, including the big displays.

The 767-400ER incorporates a new flight deck similar to that on the 777 (...) The overhead panels are largely unchanged (Boeing).