Do listeners understand different adjective orders?

I found What is the rule for adjective order?, but I keep wondering if listeners actually understand what I mean when I don't follow that order. For example, if I say, "a lovely long white coat," I may change it to "a long white lovely coat," or "a lovely white long coat."

They both sound the same to me.

Generally, when using multiple adjectives for a single noun, native speakers will start with the most general and subjective adjectives in the front, and work their way down to the more objective and specific adjectives.

In your examples, "lovely long white coat" sounds the most natural, as it goes from subjective and general ("lovely") to a bit more descriptive and objective ("long") to even more specific and focused ("white")

However, note that sometimes an adjective pairs with a noun to essentially create a new noun, so you'll want to keep those together. For example, "long johns" are a specific type of garment, so saying "long white johns" would sound very strange.

To answer your specific question, yes, native speakers would understand your meaning regardless of adjective order. There is a standard adjective order in English, as you're aware, but I'd be willing to bet that the vast majority of native speakers have never thought about it, aren't consciously aware of it, and are perfectly capable of understanding a sentence or phrase that doesn't follow the standard order. In fact, some poets have used different adjective orders for interesting effects (sorry, I'm at work and don't have any examples readily at hand).

At worst, it might take someone a couple of extra seconds to parse your sentence, to consider whether (as Peter Schor suggested) a long coat is a specific type of garment that's being described as lovely and white. Some people might take a moment to mentally rearrange the words to the more common pattern. If I heard the phrase "long white lovely coat", I might briefly wonder if I'd misheard, and the speaker was actually speaking of a long white overcoat. Still, assuming I heard the words correctly, it's very unlikely that I'd fail to understand the meaning.