Does a REL subwoofer make the speakers' job easier?

1.  The sub would make the speakers’ job easier by not sending the low bass signal (i.e., below the crossover point) to them.

This can be true as long as the crossover in question has high pass filter capabilities. A feature very few powered subwoofers posses. A couple of exceptions are the JL Audio “E” series and I believe the Audio Kinesis “Swarm” (actually passive subs with an external amp). The other option would be to use an external crossover connected to your preamp outputs, which would split the signal that feeds your main and sub amps. Some examples of these would be the JL Audio CR-1, miniDSP as well as units made by dbx and XTA.

2. The signal sent to the speakers would still include the low bass even when the sub is used. Therefore the speakers would still receive the full range signal.

This is true with the connection method that you present.

Option 1 makes the job of your main speakers easier, option 2 does not.

The only sub that I know of that uses a high pass filter is Vandersteen.

And, yes, by utilizing the high pass crossover, the amp will be relieved of power demanding low frequencies.

B

I have a REL Storm subwoofer in my system. The REL subwoofer gets a full range signal from the amp. The subwoofer presents a very high impedance load to the amp, the amp acting mainly as a voltage source here. That is why the signal cable from the amp to a REL subwoofer has thin wires. The main speakers have the full power and full range of the amp, no loss to the tiny trickle taken by the subwoofer. The subwoofer gets exactly the same signal as the main speakers, so integration occurs naturally. I positioned my REL Storm near my listening position. It integrates like mad. I asked an experienced audio listener at my house if he thought I had a subwoofer in my system. He did not think so, even though that huge downward firing Storm was standing four feet in front of him. When I told him I did have a sub, he could not point to the source of bass. I am very happy with that arrangement.

@hilde45 Great point about the phase adjustment. I do feel that granular phase adjustment makes a difference for my affordable Jamo sub. But my REL sub does perform super well in its system. I wonder why REL doesn't provide more gradation in phase adjustment. 

I've run my main speakers full range with a couple of RELs for years and it sounds great. "Classdstreamer" answers his own question with 'my REL sub does perform super well in its system." Subs don't need to have adjustable "gradation" as things are either in phase or not. REL owners rarely wonder about that. It's simple, and easy to see phase adjustments work with RELs. Good subs add that bit of reality where low frequencies exist (as in the actual world) so main speakers can seem to take on more life-like tone.