Can we have properly defined scope before the detailed project plan? I guess, this is the "best case" secario if you are the project manager who is to execute the work defined in the scope statement.
But, before a properly defined scope can be obtained, there are a lot of planning and coordination work to be performed by the team. There are many rounds of follow up to be done. There are many parties to be interviewed and met to obtain all necessary important information. So, the objective of the project plan is to include that portion of work as well.
The scope statement (some times it is known as System Requirement Specification for software project) will be a "living" document. This means that, the team will continuously update the scope document to ensure the latest and most accurate condition of the requirements are documented. When there is additional scope after further assumption clarification and exploration, this new requirement will be submitted for approval for inclusion as Change Request. When we say new requirement it means that it is totally outside the original intention of the requirement. For example, originally the scope statements specifies that there are two units of servers are required for hosting the database. After the project is started, some external government authority dictates that for all transaction audit, the system needs additional two units of servers to store archive-data. In this case, the two additional servers are considered as new requirement.
In another scenario, in the original scope statement, if it reads "The system shall be able to keep the sales transaction for 3 months on the production server." After further study, the team finds out that the "sales transaction" means sale enquiry record, quotation record, sales order record and payment record. But, the original team assumes the sales record is equivalent to sales order record only. In this case, the problems arise: For these four types of records, for three months, the production server storage capacity is not sufficient to store these records. So, additonal storage media or shorter duration of the record keeping needs to be decided. In this scenario, it is "wrong assumption or intepretation" of scope definition. It is not an additional requirement. It is an under-estimate of scope complexity. In this case, it is the vendor responsibility to "find out" what does "sales transaction" means, what to do after the "3 months", and where the "production server" is.
Then the next question will be, how can the vendor find out this requirement in a very short duration during tendering (or proposal) stage? Usually, the detailed study will be performed only after the contract is awarded to the vendor. But, the tolerance level for scope difference should be defined in the project flexibility. Some times, the buffer for the scope is built in to the quotation or proposal. It is part of the risk assessment. The buffer for wrong estimate is crucial especially for fixed price contract.
So, the conclusion is ... it is very rare chance you will have a properly define scope before you start developing your detailed project plan :-)