Is it possible to use Angular and still be Lightning ready?

You can use Lightning Components as a container for your angular applications but not use any of the other functionality they provide. Using Lightning as a container instead of Visualforce gives you access to all the interfaces (https://developer.salesforce.com/docs/atlas.en-us.lightning.meta/lightning/ref_interfaces.htm) that allow your components to be accessible from many contexts inside Lightning Experience. This will likely allow your components to integrate much more smoothly into your user's Salesforce Workflow (instead of having to make a custom Visualforce tab for each component, for example).

There are a number of posts out there about using Angular in Lightning that you may find helpful and my understanding is that as LockerService is maturing it is no longer a barrier to using third party libraries that need DOM access for rendering.

If it is for lightning Ready badge for appexchange ,you do not need anything more except to use SLDS as a CSS skin .Take a look at this to understand what is lightning ready .It need not be true lightning components .

The other alternative is to iframe visualforce inside the lightning component .