Not if the application names differ. You could use a wrapper object from the cbstorages module to encapsulate all session storage.
In reality, I would recommend you re-think the two-app structure and move to
a single CF application
a single ColdBox app
Two ColdBox modules with entry points /public and /manager respectively.
Now, not only can your two apps share the same session, but they can also share all ColdBox settings, models, modules, you want. ColdBox modules basically provide you with the closest thing to separate apps but still actually a single app. Each module can still have its own