No. At ArcGIS version 8.3, checked out data cannot be edited in a personal geodatabase with an ArcView license. The editor prevents this. In order to edit a check-out geodatabase, use an ArcEditor or ArcInfo license.
At ArcGIS version 9.0 or higher, it is possible to edit checked out data in a personal geodatabase with an ArcView license. The editor does not prevent the personal geodatabase from being edited because it is a checked-out geodatabase. However, it still applies the same rules as non-checked-out personal geodatabases. For example, topologies cannot be edited with an ArcView license, but simple feature classes can be edited.