If I delete a submission from this site, will it automatically delete from the integrated google drive, and vice versa?

No. The submissions deleted from JotForm will not be reflecting in Google Drive. The integration to Google Drive is one way and it allows only to push the submissions. If you want to delete the submissions from the Google drive, you'll need to delete them manually from the drive. 

Hope this information helps. Please let us know if you need any further assistance.

Thanks!