The short answer to your questions is no, but the reasons why are pretty important in the context of distributed databases using ESRI technology.
Here is the ESRI help document on Creating a One-way or Two-way replica.
What is important to note is that a Two-way replica can only be created when the replica is an SDE Geodatabase. You cannot use a Personal Geodatabase in a 2-way replica. There are two ways to have an SDE Geodatabase. The first would be to use the SQL Server Express installation that comes with an ArcINFO License of ArcGIS. The other would be to simply add on to an ArcGIS Server installation.
An important question would be why you want to have an offline application that would be synced and merged in both directions that didn't have any versioning in place? If you are working with an application where data is being edited by multiple users, versioning is critical for maintaining data integrity. The Replication and Versioning process through SDE are what ESRI uses to validate data between different users and the base dataset, and also, and potentially more importantly, to allow an Administrator to resolve conflicts in cases of two or more people editing the same feature.
The way that you could get around this, is slightly complicated from a management point of view, but it will work, and maintain data integrity. You can create 1-Way replicas that are in Personal Geodatabases. If you created a number of these, then users could perform edits and synchronize from the Replicas in to the Parent SDE Geodatabase. Since this is only going in one direction, the PGDB's would eventually get out of synch with each other and the Parent GDB. So, on a set schedule, you would need to drop these replicas and create new 1-Way replicas to PGDB's of the same name. This way, you wouldn't have to repath any data in your application.
The volume and frequency of edits would determine how often you would need to recreate these replicas.