Are modern aircraft (fully loaded and fueled) able to operate from hot and high airports?
1. Thrust / FADEC
FADEC does not increase the thrust of jet engines. If anything it limits the thrust; the MD-11 has an emergency power overboost bar that disables the FADEC protections.
(YouTube) Instructor holding the aforementioned bar.

Whereas in crisis (for example, imminent terrain contact), a non-FADEC engine can produce significantly more than its rated thrust, a FADEC engine will always operate within its limits.
— Wikipedia

2. Lift
Aerodynamic advances sure help. But they can't make the air denser. Hot and high conditions still limit aircraft performance.
3. Tires
Tires are better now, but even with an extremely long runway, they can't withstand the speed needed to lift off fully fueled and loaded from a hot and high airport. (Higher speed is needed because of the thinner air and high takeoff weight.)
4. Number of engines
The more engines you have, the better performance you get, namely if an engine fails on takeoff, you'll have more power left on a quad-jet versus a twin-jet (3/4 vs. 1/2).

MD-11
In this answer, you see the MD-11F needs to stop for fuel mid-journey because it takes off from a hot and high airport.

The answer to the main question is no—the tires would burst at the required high takeoff roll speed given an adequate runway length and zero (hypothetical) climb limitations.

Boeing 787 (21 years later)
In this other answer, you see a not particularly high airport, but hot, limits the amount of passengers on the 787 headed from Vegas to Europe.

The first linked answer examines the physics behind hot and high, and the 787 answer examines a real life scenario with real numbers.