tl;dr - in theory, sure. In practice, I've found that it isn't really needed.

In theory, yes, one could use the hyperfocal distance (HFD from here on out) to ensure that all subjects are reasonably sharp. That being said, an important consideration for "sharpness" and HFD is the print size and viewing distance of that print. If you figured out some great range assuming a 24"x30", and then the client asks you for a 40"x60" to put above their fireplace where people will walk right up to it...well, that might not work out so well.

The use case for HFD is to get things on out to infinity into focus. Landscape shooters love it because it allows for some foreground subject to be sharp while maintaining sharpness to those distant mountains/vistas/clouds/whatever.

However, with portraits, we're typically trying to isolate the subject(s) and having some background blur isn't a bad thing. Even in environmental portraits - it's typically the immediate environment that you're showing off, not what's hundreds of yards (or more) away.

Consider this image (click to expand) (Shot by Redfield Photography):

There's obviously enough Depth of Field due to the aperture, focal length, and distance to subjects to get them all in focus - but not enough to get the background. So, this is not using the HFD. And, this would be a worse off picture had the shooter decided to use the HFD, because the background trees would serve no purpose being in focus.

Even with groups of people, like a high school marching band...something like that would necessitate using a wider angle lens from a distance, where DoF comes easy; the need for HFD is simply not there.