If this is for live performance then using one mic will strongly limit the overall volume of the system. The mic's greater distance will require using more gain on the mixer which will increase the likelihood of feedback.

That said, there's a style of bluegrass performance where they stand around a single large diaphragm mic such as an AT4030. They don't use monitors since they are close enough to hear each other acoustically. Such groups can't get as loud as those with separate mics for everything, but that is generally accepted for the style of music.

Other than for the carefully-staged Bluegrass usage that Boulder mentioned, the combination of a single mono mic positioned to pickup two different sound sources and feeding a PA system in a live environment is usually a recipe for disaster. Add to that any form of compression or AVC and it becomes even worse.

The only effective way you can make a single microphone system work for vocals and acoustic guitar for recording (not feeding a PA) is to use something like a stereo ribbon mic or other stereo type that has two orthogonal fig-8 responses and position it horizontally in front of the performer so the performer's mouth and the guitar soundhole subtend a right-angle at the mic. This effectively gives each sound source its own mic with the other source in the nulls of the response. You then have two mono channel outputs that you blend into a usable mono or stereo image.

As an alternative, what I used to do when performing (which I rarely do these days) is to have a DPA 4099G microphone clipped to the guitar and for vocals use a Sennheiser headset mic. These fed two independent radio packs, but could equally well have been cable-wired to the mixer if I had not needed the freedom of movement. I got almost no bleed from one mic to the other since the source to capsule distances were so short. In addition, since the sound source-to-mic distances were fixed and repeatable, I could pre-set the gains and EQ on my small mixer knowing that only the single master output to the house PA might need any adjustment between venues.

I would recommend your friend try this route of headset mic and attached guitar mic to get a simple system that is high quality, low bleed, virtually feedback-proof and moves from venue to venue with no adjustments to the balance and EQ. I also got an almost identical sound in each venue. This technique does need quality components to work well, so is not the lowest-cost arrangement, but you have to put a value on your ease of setup, consistency of sound and peace of mind.