Nope, LEDs operate on current, not voltage. They will quickly avalanche and run away of the current is not restricted. There is such a thing as a constant current source, using something like that set to a value below the LED’s limit would allow the LED to be connected without a resistor.
So-called “12V LEDs” are just ordinary LEDs with a resistor already inside.
Essentially what happens is that once the LED conducts, it allows more current through. This allows it to conduct more…so more current goes through. Until it gets beyond the limit for the particular design and chemistry, and the junction is fried. Resistors in the circuit work because of, once again, Kirchoff’s Laws. Two devices in series combine voltage, and two objects in sereis share current. LED (and regualr diodes too) have a set voltage drop, at all but the extremes of their operating range, this voltage drop is always the same (in reality, there is a very sharp curve once the limits are exceed, for the practical purposes that we are using here, we can assume it’s a constant). This is part of the LED spec. Common for a T1 or T1 3/4 size red, green, or yellow LED is about 2.1 volts, but always check the specs on the ones you buy. Typcal white LEDs are more like 3.5 volts. By applying Kirchoff’s Laws to our circuit of a power supply, LED, and resistor, we find that the sum of the voltage through the resistor and the voltage throught he LED must equal the power supply voltage. So if there is a 12V power supply, and the LED drops 2.1 volts, 9.9 volts must drop across the resistor. We also know that if we want 15ma in the LED, then the resistor must also have 15ma of current flowing through it. We now know the voltage across the resistor, and the current through it. Ohm’s law provides us with the missing piece - how many ohms must the resistor be. Ohm’s Law says E(voltage) = I (current) x R (resistence). Dust off that algebra, and solve for R, and you get R=E/I. We know E, 9.9 volts. We know