Is it acceptable in American English to pronounce "grocery" as "groshery"?

I can tell you it's one of the versions mentioned (the last one)

gro·cery
noun
ˈgrōs-rē, ˈgrō-sə-rē; ˈgrōsh-rē

by the Merriam-Webster Dictionary

I also have heard it this way in Canada.

It's also mentioned here in Wikitionary:

(General American)
IPAA(key): /ˈɡɹoʊsəɹi/, /ˈɡɹoʊsɹi/, /ˈɡɹoʊʃɹi/

Sat., Ap. 16, 2016 3:51 p.m. PDT

American English pronunciation of “grocery(ies):

In well-spoken American English, the words “grocery” and “groceries” are pronounced in two ways:

Gro-sir-re (in three syllables)

Gros-re (in two syllables).

You can hear those pronunciations over the internet in audio pronunciation websites.

Most of these give a three-syllable pronunciation of "grocery" and "groceries".

I am a native Los Angeles resident. I pronounce “grocery” and “groceries” in the two-syllable way, gros-re(s).

This is MY opinion. There is NO “sha” in the words “grocery” and “groceries”. The “c” is pronounced as a soft “c” with an “s” sound.

This is MY opinion. The pronunciation “groshary” is incorrect. I think that mis-pronunciation implies the individual has a speech impediment (a lisp or a stutter), has loose or missing teeth, is just learning to speak English, or is pronouncing those words in a patois or slang. It is not the main-stream educated American English oral form of the word. 3:51 p.m. PDT

Note that I am not trying a case in an American court in which proof by admissible evidence is required.
I do not find in American or British pronunciation guides the "sha" sound, except for one. The words "grocery" and "groceries" come from the French word "gross" and ultimately from classic and medieval Latin.

Here are links to various websites giving audio and/or phonetically spelled versions of grocery and groceries:

http://dictionary.cambridge.org/us/pronunciation/english/grocery

http://www.macmillandictionary.com/us/pronunciation/american/grocery_2

This Boalt Hall lawyer rests her case.

Both--GROCERY and GROSHERY--are correct. There is always another way of pronouncing the same word.

Lexico gives the transcription /ˈɡrəʊs(ə)ri/ (GROCERY) for "grocery". Is there anything in the transcription that draws attention?

In "casual" speech, unstressed schwas are usually chewed off; /ˈɡrəʊs(ə)ri/ → /ˈɡrəʊsri/ -- I removed the schwa.

Now there's another thing that catches my eye. Does it catch your eye too? I suppose not.

It is the /sr/. The consonant /s/ is called an alveolar sibilant; it's produced at the alveolar ridge--the bony ridge behind the top teeth--and is characterised by a hissing sound. The /r/, on the other hand, is a post-alveolar approximant.

In casual speech, we make the sounds that are next to each other more similar to each other (aka assimilation, which is a very common process). The /s/ is originally an alveolar sound, but when it's followed by a post-alveolar sound, we tend to make it similar to the post-alveolar sound. Assimilation can be described by this example: this shoes - how do you pronounce this phrase? In casual speech, it is nearly always [ðɪʃʃuːz] rather than [ðɪsʃuːz]. The /s/ changes its place of articulation because of the following /ʃ/ to make it easier.

When the /r/ comes right after the /s/, the /s/ becomes more like the /r/. In other words, the /s/ changes its place of articulation--which is alveolar--to post-alveolar (back of the alveolar ridge). In post-alveolar region, we have another sibilant /ʃ/ (the SH sound), so the /s/ changes its place of articulation from alveolar to post-alveolar and becomes /ʃ/. That's why you pronounce it [ˈgrəʊʃɹi] (GROSHERY) in fast speech.

The word "issue" used to be pronounced [ˈɪsjuː] - IS-YOU in Britain (most Brits still pronounce it that way!), but due to the same phenomenon, people pronounce it [ˈɪʃuː] - ISHOO.

It is surprising that this assimilation only happens in "grocery" and not other similar words like "nursery", "serene", "sorcery" etc. Maybe it will happen in those words one day.

Hope that helps!

I have always pronounced this word as GROSHERY, and after much research, I have found that this pronunciation is both prevalent and widespread.

I consistently check YouGlish.com before offering my own pronunciation of a word to my ESL-students as a "standard" one. I have found this to be extremely useful as there are so many variations, and I consider it due diligence on my part. In many cases, I find that what online dictionaries depict does not reflect the true usage (using the thousands and sometimes hundreds of thousands of videos available on YouGlish as a reference). I would argue that before anyone belittle a particular pronunciation of a word, they check this site and verify that they are not being obstinate. Languages are fluid and ever-changing. If you consider yourself a true linguist or language-lover, you must be open-minded to such shifts and changes.