When you break a connection, you lose the binding between the input elements and the control over sub-elements.
The standard steel connection or parametric cut which composed a custom connection remain in place and unchanged.
Annotations (tags and dimensions) placed on connection elements will be kept after the connection is broken. Only the tags placed on profiles that are part of connections will be lost because those elements are transformed into structural framings when you break the connection.
The Break tool is not available if one or more connections in the selection are generic connections or failed connections.