They can, but for a variety of reasons it doesn’t feel right. The piano may be much louder than an acoustic guitar and fills a lot of acoustic space in terms of pitch, timbre, resonances, and harmonics. Numerous acoustic guitar sounds are so similar to piano sounds that they are readily overpowered. That’s a guitar and an acoustic piano in a space without any amplification.
The images vary a little bit when they are magnified. In order to give each signal space to be perceived in ways that complement the other, the signals of each can be equalized to de-emphasize conflicting frequencies.
The method is the same whether combining lead and backup vocals or bass and kick drum. Panning is also quite helpful when recording.
When I initially saw the question, I immediately thought of two things. First, I thought back to a live, unplugged acoustic performance that my friend and I gave while playing a grand piano. We were performing original songs and discussing the background information about them. We would frequently sing in unison while we played together. The performance went well, however due to the lack of clarity in the instrument pairing, all I was able to play behind her was a very simple rhythm part.
The amazing acoustic guitar and electric piano fusion on Warren Zevon’s song “The Hula Hula Boys” also sprang to mind. Although they aren’t much EQ’d, the stereo separation maintains them apart. If you want to hear it, it’s available on YouTube.