We disabled the text selection in our Dashboard Grid item. However, it is possible to enable it by setting the "user-select" CSS rule to text for rows. I suggest you refer to the Web Dashboard - How to allow end-user to select text in a grid cell thread where we discussed a similar task.
I hope this information will be helpful.
I also want to note that with the next major release we have removed the old DashboardViewer component and we will no longer add new features to it. Please refer to the How to migrate from ASPxDashboardViewer to ASPxDashboard working in ViewerOnly mode KB article to learn more about migrating to a new ASPxDashboard component. So, I suggest you get started to use the new ASPxDashboard component if you are planning to update to the newest version.