As Greg said, there's no direct SEO ranking impact by including keywords in your GMB posts.
HOWEVER, keywords in GMB posts can be pulled up and highlighted in the map pack which
may positively influence CTR %, which
may in turn positively influence your search ranking.
To take advantage of this, we use Google's GMB API to automatically post every customer delivery photo as both a photo and a post on our GMB profile. In the GMB post text, we reference the vehicle purchased and where the customer is from.
You'll see an example in the screenshot below:
View attachment 5822
We were one of the first ones on the GMB Post bandwagon a few years ago back when they were still featured prominently above the fold. We used them effectively to promote our monthly offers and saw great results.
However, that didn't last long because as soon as Google pushed the GMB posts below the fold, our GMB post impressions and clicks dropped off a cliff to basically zero. This is about when all of the OEM's learned about GMB Posts (always late to the party) and pitched them as a miracle solution to sell a ton of cars - which of course is not true.
So we shifted our strategy away from monthly offer posts over to these real-time delivery photos and experienced significant organic growth. Was it because of this? Who knows, but it certainly can't hurt especially with how few people view and click on the average dealership GMB post to begin with.