Yes and no, the behavior is typically dependent on the authorization process of the app. For example, Jawbone only allows one Jawbone account synced per user under the same organization. Syncing the same Jawbone account to another user under the same organization invalidates the previous authorization granted under the first user who then would not be able to receive new data. Runkeeper, on the other hand, allows syncing a single account across multiple users under the same organization.
See the table below for which apps allow a single account to sync to multiple Validic users and which apps do not.
Table: Syncing an Account to One or More Validic Users