Kendall Walton, in his fascinating aticle "How Marvelous! Toward a Theory of Aesthetic Value" suggests that they cannot, or at least for the most pat do not. (in his Marvelous Images: On Values and the Arts, Oxford University press, 2008 3-21...originally JAAC article). He says "Participation in children's games of make-believe doesn't demand or even encourage judging the value of props, or games (types or tokens), or participants, or acts of participation....Children don't endeavor to perform well, in participating in their games; it seems out of place to judge that one child did a superb job of playing dolls..." (6) This is right as it stands but perhaps a bit deceptive. I remember back to playing games where we dressed up as pirates and turned a piece of furniture into a pirate ship. Surely in putting together the costume or the selecting the object to serve as a "ship" we judged some to be better than others: that looks good, that does not. The quality of the prop might well have enhanced our playing experience: some pieces of furniture just work better as pirate ships. Moreover, some kids just are better at playing than others: we know this because they select playmates. Also, some play sessions are better and more fulfilling than others. Following Dewey, one could say that some examples of playing games count as "an experience" and some do not. The ones that do would count, for Dewey, as aesthetic, and the ones that do not would not. Of course Walton doesn't say that this never happens: he just thinks that evaluation doesn't happen, and for an experience to be aesthetic aesthetic evaluation has to be present. This all relates to everyday aesthetics of course. When I wrote The Extraordinary in the Ordinary I had forgotten about Walton's essay, although I must have heard him give it since I was at the Summer Intitute in the Histories of the Arts in San Francisco when it was originally given. The work is actually quite significant for everyday aesthetics since it seeks to distinguish between aesthetic and non-aesthetic pleasure. It doesn't exclude the possibility that everyday experiences can be aesthetic, but it does definitely draw a dividing line.
Consider what he has to say about folk art. Walton says that many folk art traditions are like children't games of make-believe. "People may participate in singing or dancing or acting, or watch with interest and enjoyment as others do, without it ever occuring to them to ask how good aesthetically the performance or the work performed is, or whether it is better or worse than another one." (7) And this, on his view, would indicate that they are not having an aesthetic experience, for that would involve an aesthetic pleasure and that must have as a component "pleasure taken in one's admiration or positive evaluation of something" (13). But surely gaining pleasure from watching someone else dance involves an implicit evaluation that the dance is worth watching. Why does one have to consciously state to oneself that this is good or better than something else for the pleasure to be aesthetic? I think Walton is right that there is a reflective element to aesthetic pleasure, but the reflective element might be much more widespread than he makes it out to be.