Yep, you place a construction site, activate it with F until it's set for healing tent, then add construction material (fire it on the construction site). Make sure you are alone at the site or some moron will switch the healing tent selection before you can add material, and the site will be fucked up.
A healing tent takes 25 construction material to build, so better get some buddies with material, too, or you will never construct it in time.
The tent actually works quite well, the only problem is it's too easily destroyed.