In Alpharad's "battle royale" King K. Rool Video, I see multiple occurrences (here's one) of down-throw (burying the opponent), jump, and up-special for some very early kills (especially on platforms). Is this a true combo?

I suspect that one has to time the jump based on how much the opponent mashes, but I'm not sure.

No. The big reason is that, given you are on the same platform, Up Special's hitbox is too high to hit buried opponents. So you can't hit them until they unbury into the air. In the link you posted, it only comboed after he both unburied and missed with Back Aerial! This was also pre 2.0.0 patch which lowered the Up Special horizontal hitbox.

When they unbury into the air is highly dependent on opponent mashing, which even at 0% can cause at least 17 frames difference in unburying. So you have to call when they enter the air.

You also struggle to position yourself well to hit them with Propeller pack especially since the 2.0.0 patch. You need to jump and lean forward to get close enough to hit them, but doing so gives your opponent time to react e.g. with an aerial attack. Even if the opponent had high damage, giving you time to move next the opponent, you still need to call when they unmash. In those scenarios, it's far easier to hit with other moves like Up Tilt or Side Tilt instead, which have better damage potential, better KO potential, and can be done immediately after using Down Throw. In fact, Down Throw is a true combo with multiple moves at high percents (which are often KO confirms at these percents), but Up Special isn't one of them.

Even if you hit the opponent with Up Special, it's a move that can be DI'ed out of (more so since the 2.0.0 patch). You'll need to call where your opponent will DI in order to keep on hitting them, else they'll escape your Up Special.

In fact it's easier to hit an opponent with Propellerpack after using Up Throw than Down Throw. The opponent will be right above you and you don't need to call when they mash. They can still react before you hit them though - don't count on this against skilled opponents.

^{_{(unfortunately)}} No. Or at least not in most of those clips.

I'm going to steal from smashboards and define a "true combo" as:

an "inescapable combo." So in other words, once you get hit by the first hit of a combo, you are stuck in it unless the attacker messes up.

In this case, that'd mean that once you've been grabbed, there is absolutely nothing you can do to escape being hit by an up-special from K. Rool.

In the clip you've posted, it's clear that the grabbed player was able to get out an almost full back-air (17+ frames), which would've been more than enough time to air dodge or jump out.

However, things look a little closer at this timestamp.

When you pop out of a bury, there's absolutely nothing you can do for the first 12 frames (I've just tested this). This means there's a small (1/5 second) window immediately after the grabbed player pops out of the bury where getting the up-special would be completely true.

Of course when they'll actually pop out is dependent on the grabbed player's mashing and their percent when buried. So I'd say it's "true" if you can somehow manage to perfectly predict when they'll pop out. But of course with how small the hitbox is on the up-special (as MBorg notes), the odds of this working perfectly and being inescapable are slim.

That being said, it still looks like a fun/stylish mixup option. If you've been consistently up-tilting out of down-throw, you'll have conditioned them to mash and jump out of the bury. Then you can catch that jump (or maybe a move they've thrown out that was buffered from the mashing--like that timestamp you posted) with an up-special.