"Pausing" log shipping to allow normal DB use. Is this process valid?
Once you bring the log shipped database online you would have to restore a new full backup to restart log shipping, regardless of how long it has been. This is because you've recovered the database and cannot then restore log backups to that database.

There is no way to incrementally refresh the Dev/QA database from production with performing a full backup restore, except possibly there are third-party tools that can do this for you. You're better off working on a solution to automate the refresh of your Dev/QA environment and have this process run outside normal operating hours to reduce the impact on your team.