Generally this is a good idea as entering a turning lane is somewhat similar to a lane change and so all of the necessary precautions for lane changing should naturally apply.
If you are checking your mirrors frequently you may question the need to throw in a shoulder check and you may have a point; but there is nothing like being 120% certain that it is a safe movement and there is no way to take back a collision once it has happened.
Consider individual situations. For example, do you really need a left shoulder check before entering this left turning lane?
Is any vehicle going to be ‘sneaking up’ behind you on your left side (i.e. driving over the concrete) to enter the turn lane before you (or behind you, beside you, whatever)? I don’t think so? I have seen Ford F350’s and Hummers drive over these types of things from time to time. But you will surely notice a Hummer in your mirror would you not? Anyone who doesn’t shouldn’t be driving.
On the other hand, you have different fingers.
It is much more important to shoulder check when going into a turning lane that looks more like this.
Cars are not really supposed to drive over these yellow painted lines; but they sometimes do anyway. Another thing you may not think about is vehicles not behind you, but from the side, potentially planning a left turn from a parking lot or driveway into the same space as you. In these instances, it is a good habit to shoulder check. Just do it. It doesn’t hurt does it?
In terms of right-turning lanes – Yes it is a good idea as there may be bicycles, among other road users to check for.
Remember, always shoulder check before you move; not at the same time.