Yes. Go to Support > Tickets > Import. Upload a spreadsheet export, click "Read the columns", map them, choose options (default status and priority, a "Stop after" limit, "Skip tickets already imported", "Bring in the last reply as a note"), review the first few rows and run it. For BoldDesk there is a second step: save your BoldDesk domain and API key, then "Pull replies from BoldDesk" to fetch the conversation history.