Burgers with all the trimmings

You're probably referring to this sign

I'd agree with Laurel in the answer already given that "all the trimmings" will be recognised in American English.

An alternative expression would be "all the fixings" or "all the fixin's"

A Google NGRAM search of the corpus of American English returned the following results

The Online Etymology Dictionary says fixing is a

verbal noun from fix (v.). American English sense of "food, garnishing" is attested from 1839.

The Cracker Barrel, a US restaurant chain offers a Wholesome Fixin's menu

Now hungry restaurant-goers looking for their homestyle favorites at Cracker Barrel Old Country Store® can find them plus a whole lot more. The new Wholesome Fixin’s menu category features 11 low calorie, better-for-you choices, with fresh ingredients and full-bodied flavor

TFD's definition for with all the fixin's (fixings) is:

Rur. with all the condiments or other dishes that accompany a certain kind of food.

• For $12.99 you get a turkey dinner with all the fixings.

• Max likes his hamburgers with all the fixin's.

I guess the "Rur." means that it's a rural expression? Probably used mainly in the South.

When you scroll down, you'll see that TFD also has a references in periodicals archive where you can find actual examples of usage such as:

Not so influenced by pop culture as the postmodernists, the stories in Drinking Coffee Elsewhere entertain on a familiar, almost nostalgic level--like Sunday dinner with all the fixin's at grandma's house.

TFD's definition for "with all the trimmings" is

with all the extra things, especially with food.

• We had a lovely Thanksgiving dinner with all the trimmings.

• I look forward to roast turkey with all the trimmings.

Their references in periodicals archive for with all the trimmings returns results with UK and US English examples:

Offering up turkey with all the trimmings, plus the bonus of a Yorkshire pud, owners Les and Pam Hippolite charge just pounds 3.

Turkey with all the trimmings and extra courses available including mince pies.

Company Enables One Lucky San Francisco Bay Area Family to Get the Ultimate Thanksgiving Feast with All the Trimmings

Cost Plus World Market (NASDAQ:CPWM), a leading retailer of casual home living and entertaining products, unveils a hassle-free Thanksgiving sweepstakes where one San Francisco Bay Area winner will enjoy the ultimate meal with all the trimmings.

Merriam Webster's popularity metric is based off searches. As I said elsewhere:

On words that are "trending right now", such as "culture", it just says "trending" and for "the" it says "top 1% of lookups".

This doesn't say much about whether people know the word or not, since if you know the definition you probably aren't going to look it up.

It's not very easy to reliably know if a word is going to be known by people. Usually what's looked at is word frequency. In general, the more the word is used, the more people know what it means. However, one big drawback of this is a lack of sorting: everything with that spelling is combined together no matter if it's what you're looking for or not.

In any case, here's what frequency band the Oxford English Dictionary puts "trimming(s)" in:

This word belongs in Frequency Band 4. Band 4 contains words which occur between 0.1 and 1.0 times per million words in typical modern English usage. Such words are marked by much greater specificity and a wider range of register, regionality, and subject domain than those found in bands 8-5. However, most words remain recognizable to English-speakers, and are likely be used unproblematically in fiction or journalism.

That's not specific to American English, however. I did a search for trimmings (must be all lowercase to make sure only plural results are returned) in the Corpus of Contemporary American English and it returned 1387 hits. The entire corpus contains 560 million words, so that's like ~2.5 occurrences per million words. (You can create a free account and repeat this yourself if you want.)

All in all, I'd say it will be recognized in American English.

Typically (at least in American English) I'd think of a burger with 'all the trimmings' as 'all the way'. Your phrasing sounds a bit more...over-inflated for something like a hamburger, but it's still immediately evident what you mean. I've always experienced the phrase 'all the trimmings' as indicating a large amount of side dishes, such as 'a Thanksgiving turkey with all the trimmings' indicating that it's served with green beans, cranberry sauce, stuffing, etc.

The word 'loaded' also comes to mind, but it's generally used only to refer to baked potatoes.