Will EMI strongly affect my sensor reading
What, two conflicting pieces of advice are not enough?  Let me see if I can contradict both of them at the same time.  Well, not really.  Neither one is exactly wrong.

In principle, I'd say that converting to digital close to the sensor is the cleanest solution, but it requires that you have a place to put some circuitry there.  If that is feasible, then for this application you shouldn't need an ADC at all, just a comparator.  (This assumes that the characteristics of the sensor won't change appreciably over time, so that a fixed threshold is adequate.)

You would need to power the comparator.  If I understand correctly, you have four wires:  LED_12V, LED_Ground, Sensor_5V, and Sensor_signal.  If the LEDs are switched on and off while you are reading the sensor, then using the LED_ground for your comparator circuit ground would be a bad idea, because there will be a varying voltage drop on the ground wire that will affect your signal.  Even if the LEDs are not switched, any noise on the 12V supply will show up on this ground, which could be a problem.  If the 12V is always on, I would use this to power the comparator circuit through a small linear voltage regulator, and convert your Sensor_5V line to be a Sensor_Ground line, making sure to keep the LED return current off of this ground.

The output of the comparator would then just be fed back to a GPIO pin on the Arduino.  I say "just", but in reality you would want to have some filtering and ESD protection on this line.

The other approach, just bringing the analog voltage back to the Arduino, could also work, but to say there will be no problem because things are running at a low speed is an oversimplification.  You would most definitely want to put some fairly heavy filtering and ESD protection on the line.  Even with a hardware low-pass filter, I would plan on doing some filtering in software just in case.  This approach does have the advantage that if the sensor characteristics change over time, your software could adaptively adjust the threshold.  Remember that any noise on your 5V power supply will directly appear on your sensor signal, so make sure that is as clean as possible at the source.