Is it possible to convert a sliding drawer into a rolling drawer?
The answer is yes you can and yes without rebuilding the drawers. However your options will be limited. 

The Blum glides mentioned in another answer are awesome but they require rather particular dimensions. Specifically they require specific space available between the sides of the drawer and the cabinet, between the back of the drawer and the cabinet, and they require a particular recess on the bottom of the drawer.

Some of these requirements are minimums. Some are very specific. 

Based on your photos it appears you have neither the room on the sides nor the space in the back, it also looks like your bottom recess is too shallow. You can search for the installation instructions and they will be very informative for you.

I can imagine that it would be painful to remake the drawers when yours have those beautiful dovetails. Do you know if your friends made the cabinet? Or did they acquire a cabinet and apply the reclaimed face material? If the latter it may be psychologically easier to rebuild the drawers.

There are center mount slides that might work for you. But those can be disappointing. 

Other observations - the drawers may run fine with wax and soap and other tricks but those drawers are pine and the runners appear to be pine. The soft wood will show its weakness over time. But that might be a looooong time. In fact you might want to wait - use wax for ten or fifteen years and then deal with the slides. Seriously. By then you might solve the problem with nanotechnology. Also seriously.