At what point is it worth using a database?

A database is worthwhile when:

1. Your application evolves to some form of data driven execution.
2. You're spending time designing and developing external data storage structures.
3. Sharing data between applications or organizations (including individual people)
4. The data is no longer short and simple.
5. Data Duplication

Evolution to Data Driven Execution
When the data is changing but the execution is not, this is a sign of a data driven program or parts of the program are data driven. A set of configuration options is a sign of a data driven function, but the whole application may not be data driven. In any case, a database can help manage the data. (The database library or application does not have to be huge like Oracle, but can be lean and mean like SQLite).

Design & Development of External Data Structures
Posting questions to Stack Overflow about serialization or converting trees and lists to use files is a good indication your program has graduated to using a database. Also, if you are spending any amount of time designing algorithms to store data in a file or designing the data in a file is a good time to research the usage of a database.

Sharing Data
Whether your application is sharing data with another application, another organization or another person, a database can assist. By using a database, data consistency is easier to achieve. One of the big issues in problem investigation is that teams are not using the same data. The customer may use one set of data; the validation team another and development using a different set of data. A database makes versioning the data easier and allows entities to use the same data.

Complex Data
Programs start out using small tables of hard coded data. This evolves into using dynamic data with maps, trees and lists. Sometimes the data expands from simple two columns to 8 or more. Database theory and databases can ease the complexity of organizing data. Let the database worry about managing the data and free up your application and your development time. After all, how the data is managed is not as important as to the quality of the data and it's accessibility.

Data Duplication
Often times, when data grows, there is an ever growing attraction for duplicate data. Databases and database theory can minimize the duplication of data. Databases can be configured to warn against duplications.

Moving to using a database has many factors to be considered. Some include but are not limited to: data complexity, data duplication (including parts of the data), project deadlines, development costs and licensing issues. If your program can run more efficiently with a database, then do so. A database may also save development time (and money). There are other tasks that you and your application can be performing than managing data. Leave data management up to the experts.

What you are describing doesn't sound like a typical business application, and many of the answers already posted here assume that this is the kind of application you are talking about, so let me offer a different perspective.

Whether or not you use a database for 700 items is going to depend greatly on the nature of the data.

I would say that, about 90% of the time at this scale, you will benefit from a light-weight database like SQLite, provided that:

1. The data may potentially grow substantially larger than what you are describing,
2. The data may be shared by more than one user,
3. You may need to run queries against the data (which I don't think you're doing right now), and
4. The data can easily be described in table form.

The other 10% of the time, your data will be highly structured, hierarchical, object-based, and doesn't neatly fit into the table model of a database or Excel table. If this is the case, consider using XML files.

I know developers instinctively like to throw databases at problems like this, but if you are currently using Excel data to design user interfaces (or display configuration settings), rather than display a customer record, XML may be a better fit. XML is more expressive than either Excel or database tables, and can be easily manipulated with a simple text editor.

XML parsers and data binders for C++ are easy to find.

I recommend you to introduce a Database in your app, your application will gain flexibility and will be easier to maintain and to improve with new features in the future.
I would start with a lightweight file based db like Sqlite.
With a well designed db you'll have:

1. Reduced data redundancy
2. Greater data integrity
3. Improved data security

Last but not least, using a database will save you from the Excel import/update/export Hell!