What happens if you don't even cut the flowers off? Do they end up falling off on their own? How does nature take care of it?

Yes, they eventually just fall off.

I don't really deadhead them in the spring.
I just grab hold of the old blooms and pull upwards and the entire flower comes off in one piece without actually shortening the stem itself at all.
Then I thin and shape however I want but the stems don't have to be shortened/pruned at all unless I choose to do so.

I also tend not to deadhead. While I do not record when do the blooms fall, I notice them thru December so sometime in January -or later- they must fall down on their own. By early Spring, I would think that if you just touch them, anything still clinging will fall.

I just wondered if you did not deadhead or prune back with the flowers fall into the bush and be a mess or would they fall into the ground?

They end up just falling off, generally sometime in spring

They pretty much disintegrate into nothing over winter for me. Then in late winter or early spring, I just cut off whatever remnants may remain.

Just wondering cuz we had azaleas in our front not too awful long ago and when the flowers died they basically fell into the bush and it ended up being a total wreck.

Feel free to pick up any parts of a plant that falls down, hydrangea-wise or azalea-wise. Picking these plant parts should minimize the chance of spreading fungi to other hydrangeas or other plants.

Another example of this disintegration magic (for me) is when hydrangeas do not go dormant and keep their leaves: after leaf out happens and the new leaves get a little normal in size, the old leaves -poof- disappear!

So I can just do nothing at all to the limelight’s? I want them as tall as possible, I heard they can get up to 14 ft if I let them go.

You can leave the flowers in the plant and they will probably drop as the bloom decomposes close to the time when a new bloom is to take its place. I have let my large bloom oakleaf hydrangeas alone with no deadheading and no pruning and the blooms drop after they bloom again in the following year. Deadheading will not affect the height as opposed to pruning which will affect the height (temporarily): cut the peduncle string that connects the bloom to the stem.

I typically cut the dried flowers off in the spring because after a long MN winter I get tired of looking at the brown crunchy stuff. Plus it feels good to get outside and do some yard work. However, I too want my Limelight to get big and it's reached the point that I cannot easily reach the top of the plant so I left the old flower heads on. They stuck on longer than I would've liked, but the new growth covers them and it didn't bother me nearly as much as I thought it would.