Can we ensure that certain modifications can only take place if an account is up to date?

Yes we have settings for Upgrades require paid invoice and successful transaction and Downgrades require paid invoice.

These two settings allow your business to control what happens when a user wishes to change their subscription and has a payment problem. This setting may not be as needed as you just start in Recurly, but can always be modified as you experience issues with subscription changes and non-payment.