Do I need to save Quicken backups that have downloaded now that I have online backups?

You've got multiple terms confused.

OFX files are NOT "backup". They're the transactions that you've downloaded from your bank/cards/investments/etc. And once they've been accepted into your Q data file, YES you can delete them.

BUT, disk files (such as your Quicken data file and OFX files) are on your hard drive … NOT stored in memory.

In general you need to store backup files (which will end QDF-backup) for as long as you feel comfortable going should your main data file (ending in QDF) fail. SO, how would you feel about having to reconstruct a week of data? Two weeks? A month? Several months?

That's a decision that only you can make. Backups are to save you from the risk of losing everything in Q, but how much shorter than that can you risk? Some folks take a backup everytime they close Q.