Hello BobMM and welcome to the forums.
I've heard such suspicions from many website owners, but many, many others have installed GA with no ranking change at all, even though their bounce rates and so on were very poor. I'm pretty sure this can only be a coincidence.
I doubt very much that Google would use GA numbers to affect ranking when they cannot use the same numbers consistently across all sites they need to rank, thus comparing "apples to apples". That would be a very poor approach, mathematically.