Not really no. I've had a google email for years and years and haven't gotten a single spam message like that.
It's only when you sign up for other sites that sell your info that that happens.
I know its hard to believe but really there is enough proof all over the internet if you look it up.
Just search : Google sells gmail account info on your choice of search engine, and you will find a large amount of articles about it.
Do you really think google would offer free emails? Without ads? Google still lives off of ad revenue too, its one of the reasons they despise Adblock and uBlock.
You can believe me or not, I'm just saying this.