The short answer is "No", that's not how it works.
The long answer is more nuanced, and it depends to some extent on your requirement.
Access itself contains components to create:
Tables in which data is stored
Forms and Reports through which users interact with that data
VBA (code) which the developer creates to manipulate and manage both the data and the interface.
Tables, being only one of the three components, can be stored internally in an accdb in the built-in ACE database engine, or they can be in a different database engine such as SQL Server, or MySQL, or Oracle, and even SharePoint lists. That means it is possible to move your tables from inside the accdb into a database which is on a server. The tables, of course, won't be directly "on the server". They'll be in the database (e.g. SQL Azure) which is, in turn, installed on the server.
Users then can each have a copy of a separate accdb containing only the interface (formas and reports) and logic (VBA) components linked to those tables in the server database.