Google will not specifically mark down your site for bad grammar. However, there are a couple of reasons why automated translations are unlikely to perform as well in Google as pages written by good English speakers.
First – because the language is not generally as well-written and clear, Google may struggle to understand it as well. It may also use different words or phrases that have the same "dictionary definition" translation, but just wouldn't be used by native speakers. This means that when they type the words that they do use into Google, pages written by other native speakers are likely to use those same words, whereas your site might use different words, and that can hurt your site's ranking.
But more importantly – automated translations are usually horrible to read. It is blindingly obvious that they are automated translations, and the language comes across as stilted and unnatural, it doesn't flow or sound right, and it can be harder to understand quickly because of that. People don't want to read pages like that. If they don't like reading them, they won't share and post links to the site. If there are not many 'natural' links to your site from other sources, Google may conclude that people don't think it's worth using, and so will demote it in the rankings.
And most importantly – even if you do manage to fool Google into giving you a good ranking, it will still be horrible for people to read, so they are unlikely to bother. You'll have a very high bounce rate, very low engagement and very few return visitors. Unless your sole business case is around advertising revenue, you will really struggle to make a site like that financially viable. If you're not worried about making a profit on it, I would still ask ... why would you go to the effort of publishing pages that people won't want to read?