Can an oversized block of aluminum function as a heatsink?

The problem is the surface area not the size.  The more surface area, the more heat is shed.

mass helps in high loads for a short time (adiabatic mode) .

For continuous loads, what matters is the thermal exchange  surface (finning)

Yes it can for a short period of time until it heats up to the core temp of the processor after that it does no good.

A heat sink has fins to radiate heat to the air and a fan to blow air across the fins.

There is a complex calculation to determine the size and shape of the heat sink.

The uP is attached to the sink with special Heat Sink Grease to move the heat to the sink efficiently. the grease is a very thin film between the uP & Sink. A much larger sink will cool more but it will also take up much more room inside the case.

A solid block will be much worse.

try it with a temp monitor program and watch the heat rise very quickly.

You can make an infinite heat sink by using a block of solid silver and making the length 10 times the area if the uP attachment. very large and very expensive. The attachment between them should be Diamond film.

Yes. A large VFD is cooled by large finned block of Aluminum. Iron too slow, Copper too expensive.

The large block of aluminum is actually a less efficient way to cool the microprocessor.  It has less surface area and that is what is needed to dissipate the heat because, as others have said, you need to eventually transfer the heat to the air. Fins in heat sinks have more surface area to do that exact thing.

yes - but where does that heat go? The block can't heat up indefinitely - it would melt eventually.  It will come to thermal equilibrium with its surroundings which may result in the processor trying to run at a temperature higher than it is rated for.  That's why you usually see fans inside of computers even though the processors are heat sinked.  THe sinks have fins that exchange heat with the air forced over them by the fans so that the processors run at a suitable temperature.

Absorb yes, dissipate, no

That is why heat sinks with fans are used instead

and BLACK heat sinks are better than bare aluminum ones