tl dr - Yes to mileage; no to wear.
Would you get better gas mileage?
The general rule of thumb would be to run your vehicle in the highest gear possible without lugging the engine. This means if you can drive down the road at 1000rpm at 20mph, you will get better gas mileage than you will driving 20mph at 1500rpm. When you try to accelerate in the higher gear, this is where you will experience higher fuel consumption because you will need to be on the accelerator longer in order to obtain the higher speed. This is due to the lower torque available to the rear wheels. In a lower gear, relative torque is increased and you will gain your higher speed faster with the same (or less) amount of throttle input, which means you can upshift your transmission and get your RPMs down again.
Would it wear out the engine or transmission faster?
Just cruising at the lower speed in the higher gear will not incur any extra wear to engine or transmission. In fact, you'll see less wear due to running the engine at a lower speed. That difference will not be much of a difference, but there will be a difference.
If an engine is ran within tolerance (normal driving) for it's entire life, maintenance is kept up, and all else is normal, it stands to reason that there will only be so many revolutions an engine will make until it is worn out. If there is a set amount of revolutions an engine will make, running it at a lower rpm at the same vehicle speed will help it to last longer.
To reiterate something, though ... all that I wrote is dependent upon your premise of a flat road without stopping or accelerating. When you throw any hills, slowing, or speeding up into the mix, all bets are off. Downshift as needed so you aren't putting undue strain on your drive train.