Can iPad be the only monitor for a Mac Mini?

For the most part, everything we do on the computer can be done with the iPad. However, there are a few applications for which we need a computer running something other than iOS. What we'd like to do is for each member of the family to have an iPad, which would work for 95% of what we do, and then have one Mac Mini that anyone could use for those applications that don't work on an iPad. We don't really want the kids using a MacBook, because they are too fragile, and we don't want a monitor permanently sitting around the house. I've seen software that will turn the iPad into a monitor for the Mac Mini. Can this work as the only monitor? I"m envisioning the MacMini sitting unobtrusively somewhere in the house so that any of us could "plug in" (either wirelessly or wired, not sure how that works) to it with an iPad when more computer power is required. The MacMini would never be used with anything other than an iPad as the monitor. Is this possible? Thanks!