Perhaps - but it has always been prudent to keep redundant copies of anything important since before computing platforms existed. Frequently backup your data and test the backups.

The bigger problem here is not really about the content, but the means. If all e-mail communication goes through Gmail (and maybe a bit via Outlook and some remnants of Yahoo), at some point you may lose your ability to communicate with the rest of the population unless you subscribe to one of these services. This is already happening to some degree but is definitely getting worse.