No, it's not.
When lifting the other character you are either taking an action, or you interacting with an object -- depending on your DM's rulings.
If the DM rules that the pile driver is an attack (which I'd argue it is), that would cost you an action, and you can only repeat it if you have movement and an action to spend on it. This assumes you've grappled them, and have an attack left.
If the DM rules you are use an object. If it wasn't an enemy, you'd only be allowed to pick it up once. Once you drop it (which is free), it is no longer a free action to pick it up again. Use An Object action:
You normally interact with an object while doing something else, such
as when you draw a sword as part of an attack. When an object requires
your action for its use, you take the Use an Object action. This
action is also useful when you want to interact with more than one
object on your turn. (PHB 193)
Since you can't lift someone and do something else, it might take a full action to lift someone above your head. Remember that a round is 6 seconds, dropping someone more than once (or twice if you have the actions for it) would take about that long. Moreover, really can't lift someone and jump while doing something else, so it could be argued it can't be an interaction and must be a "Use Object" action.
To rule otherwise would allow a free 5d6 damage without using any action, and that, while awesome the first time (and a DM may allow it once, by Rule of Cool), is game breaking.
As RAW, no, it does not
Being considered a size higher for carrying capacity and push, drag, or lift force is not the same as being a size higher for all purposes, including grappling.
You count as one size larger when determining your carrying capacity
and the weight you can push, drag, or lift.
As RAI, maybe
The loop hole is that the PHB has no reference on why and how the grapple-er can move without speed penalty if it is two size higher, and the DMG does not touch the subject. There are two potential scenarios for why a grapple-er one size or lower has it speed reduced, though; the grappled creature have enough leverage to make the movement difficult or that the grapple-er cannot carry comfortable enough the grappled creature as in "difficult terrain", and that the weight of the creature is the deterrent.
In the first case, since Powerful Build does not increase per-se the size, it is safe to assume that it does not help to increase the comfort or reduce the leverage and, such, the speed is halved.
In the second case, where is the weight that maters, things change. Powerful Build improves the carrying, dragging, and lift capacity, therefore the grapple-er creature does not have its speed halved.
Which one it is
The only evidence I found is in favor of is that weight is the reason for the reduction in speed. The first part is in the text of moving a grappled creature (emphasis mine).
When you move, you can drag or carry the grappled creature with you,
but your speed is halved, unless the creature is two or more sizes
smaller than you.
As far as I can tell, there are no rules on how you drag or, particularly, carry a grappled creature. You can carry over you head a grapple creature as if it were a sack of potatoes. In PHB 176 there is a segment that shows how can you drag, carry and lift something in particular and, as shown, it is a STR and weight contest in which Powerful Build should work as intended.
Push, Drag, or Lift. You can push, drag, or lift a weight in pounds up
to twice your carrying capacity (or 30 times your Strength score).
Bottom line
At the end is the DM that has the last word. Talk to your DM and present the evidence. If you are the DM decide what it is best for your campaign. If a particular decision is more powerful that you expected it is in your right to take back the decision.
Best Answer
This is a slightly foggy area...but thankfully, Jeremy Crawford (official voice of rules for WotC) has weighed in on this in several (indirect) ways...
https://twitter.com/JeremyECrawford/status/729784756255100928
Additionally, in relation to grapple/drag...
https://twitter.com/JeremyECrawford/status/907788900998946816
So, this gives us a baseline to build on top of.
Crawford has said that you can carry a friendly (and thus, willing) target around with you using the Lifting and Carrying rules. This seems rather evident, because horses don't have to grapple you to carry you (or someone you captured and threw over their haunches) around. Additionally, giving someone a piggy-back ride is not at all like seizing someone in combat. Furthermore, he states that the Lift/Carry rules do not apply to Grappling.
From here, we don't have any further clarity from the developers, but we can move on to plain English definitions to clear things up. Because that was the intent of D&D 5E is that plain English definitions could be used to help adjudicate the rules.
Mirriam-Webster Dictionary
Based off this definition, we can work out what 'grappling' is. A "Grapple" is when you have seized someone who does not want to be seized. They are resisting you and trying to get loose.
If someone is not resisting you, you are not grappling with them. If someone is not capable of resisting you, you are not grappling with them. You're just holding them. Throwing an unconscious or willing individual over your shoulder is not grappling, that's carrying.
Thus, the ruling that makes the most sense, based off both Crawford's rulings, simple definitions, and logic--is this:
"If a target is unwilling, you are grappling them. If the target is willing or unable to resist, you are carrying/dragging them."