The RDS service is literally scripted EC2 instances running MySQL/Postgres/SQL Server etc. Anything you do in the RDS console/API runs (or schedules) scripts on EC2 instances. If you would have downtime on any maintenance of your self-managed DB instance (say, upgrading the DB engine), so will RDS.

Some people get disillusioned at this fact, thinking RDS was something more magical. But AWS does offer the Multi-AZ option, which does the maintenance on the standby, fails over, and then performs the same on the main instance. It's effectively transparent. RDS also makes backups, restores (including point in time), encryption using KMS etc. really easy. If you don't have a full-time DBA, RDS provides for a very easy to use DB with virtually no maintenance required, but Multi-AZ is absolutely required for any kind of production deployment.

AWS's answer to Cloud Spanner is much more likely to be a future cross-region replicating version of DynamoDB or Aurora, not RDS.