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

I caught myself pronouncing the "c" in "grocery" as an "sh" sound. Is this commonplace/accepted, or is it perhaps geographic? Does this occur with "c" in other words?

As background, I was raised in Cincinnati, OH and now live in western New England.

This will be a fairly common pronunciation. It is caused by the influence of the /r/ which follows afterwards. In the word /ˈɡroʊsəri/ there's a schwa between the /s/ and the /r/ - in bold in the transcription. This weak vowel can be omitted altogether. When this happens our mouths will be preparing for the forthcoming /r/ before we actually make the /s/. Our tongue has to be slightly retracted to make the /r/, and so when we make the /s/ it is further back from it's normal position. It moves towards a post-alveolar position giving it a /ʃ/-like quality. [/ʃ/, of course, is an unvoiced postalveolar ficative].

The more likely you are to use a schwa sound between the /s/ and the /r/, the less likely this will be to happen.

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/