When an application or website not listed in the excluded list is accessed there could be a situation where an embedded application could be from the excluded list (E.g.: A learning app having Facebook content /authentication). Will I be able to access that?

You will be able to access the excluded application from any other data plan or will be charged LKR 0.3 per MB for excess usage charges. If such is not available you will not be able to access the embedded application.