Your pros and cons are spot on. So, if you have the time, I would create a responsive design. Wider screens leave the pane open with labels and then when room is limited you can collapse to just icons.
But a warning about "icons only"...I have had first hand experience with this and what we found is that from a usability perspective "icons only" has too much cognitive load for the user to remember what all the icons mean. We had a small side bar navigation UI like you mentioned and had about 9 icons for a user to switch between. Based on feedback and usability research, our design changed from an icons only side bar model to a text only horizontal model. Luckily this worked because the product was desktop only and real-estate was not an issue. Here was the blog post that announced the change for this feature. https://blogs.msdn.microsoft.com/ie/2014/12/09/announcing-the-redesigned-f12-developer-tools-interface/
And a user comment.
As you can see, the cognitive load of remembering icons is very real so I think this is a band-aid that unfortunately won't help in the long run:
The con can be solved by giving a tour initially , or another counterpoint is that the users who use the dashboard will get acquainted with the UI in a week or so.
Your user might remember an icon briefly, but it takes a long time for users to learn icons. If you have 3 or less icons then that might be okay cognitively, but users have a hard time remembering the meaning of many icons and create mental shortcuts in their brain to remember the general position of the icon when thinking about where to click. What ends up happening is users often misfire on an icon just because it's close to another icon, because they don't know the icon, they just know it's "somewhere down here."
Again, to balance mobile/desktop needs, I'd recommend something responsive that takes the best of both worlds. At it's core this is an icon readability issue so this is good reading. :) https://www.nngroup.com/articles/icon-usability/
