Yes and no,
I'm afraid it really is one of those things. There are all kinds of issues with the 'master project' approach. Not the least is security, though Sparx recently added the ability to secure projects in this scenario.
The basic process is just what you fear. But there are considerations both ways.
Each "model" in an EA repository is a tree descending from a root element. All models have one root item by default, which you can rename but not delete. You can create additional root items by right-clicking the top of the Project Browser tree and using the context menu.
Each such root item, and the model under it, are independent. For example, an element or connector cannot reference elements in another model (i.e. under a different root element). [Note: I do not know what happens if you attempt to duplicate an element's GUID in a different model in the same project; I don't think you should try this.]
But remember that all users will have at least read access to all your models. This might not be what you intend.
Perhaps there are other ways to ease the burden though...
Another possibility is to use a 'lightweight' DBMS for day-to-day work. If you are an Oracle or MS SQL shop then the Express versions might be just what you need. Your project manager (or whoever) could set up the working projects, and you'd be off your corporate servers. You could put periodic snapshots into a small number of corporate repositories in various ways. Your DBA could help you with automated scripts, or whatever.
Search the forum for some discussion about these issues. There are not too many threads, but there are some. You'll find some (informed) opinions, much discussion of various approaches and options, and some lessons learned.
I know that's not a cut and dried answer, but perhaps it will save you some time and grief.
David