Can we perform source control operations while the import is still in process?

Yes. It's a big improvement of VSS Import Tool in SourceAnywhere Standalone 2.3.1.

You can now work on any files/projects once their latest versions have been imported. In version 2.3.1, the import process is divided into four stages: import items, import file content, import pin status and import labels. Generally, when the import process moves to the label import stage, you can perform all the operations, except label, on the whole repository.

To learn more about the new version of VSS Import Tool, please refer to:
http://www.kevingao.net/sourcesafe/new-import-vss-to-sourceanywhere-tool.html