Whether or not the guitar (or anything else) should play "the melody" depends on the kind of performance.

It is a widely accepted rule in performance that NO INSTRUMENT should play the melody when there's a singer "playing" the melody.

An accompanying instrument can play a "counter melody," or a "different voice" (alto, tenor part etc) and can add embelishments to the extent that they don't detract from whoever is doing the solo, whether it's a singer or another instrument; but NO PERMFORMANCE should ever (except when it sounds better) have two instruments (including voices) playing the same melody at the same time.

Music publishers once offered separate "accompaniment" arrangements, especially for piano and sometimes for guitar that deliberately omitted the melody (but sometimes showed it in a separate line for reference), but with the "dumbing down" that coincided with the "everybody can sing" movement I'm not sure it's as easy now to find such scores. Separate scores were then were produced for "solo instrumental performances" so that the piano (or guitar) could play both melody and accompaniment, but the difference between the two kinds of scores was once fairly clearly indicated.

For best effect, the guitar, even when accompanying the singer who is the one playing the guitar, should not play the melody. The only time instrumental playing of a melody is permissible, according to this principle, is when the particular instrument and player has "a break" where that particular player is effectively the "solo instrumental artist" for the duration of the "break."

Since many guitarists begin by learning a few chords to accompany themselves when singing, it is the preferred performance method that they do NOT PLAY the melody while they are singing the same melody, and many never progress much past where their "accompaniment" is adequate to support their vocal performance.

And note that in a jam, many singers (and solo instrumentalists) do consider it incredibly rude if you play the melody along with their vocal/performance, so if you're polite and haven't progressed to taking "solo breaks" yourself, there are likely to be few instances in informal group sessions for you to "practice" playing "melodies," and almost no times when it's appropriate. (Some vocalists consider it rude if you play anything while they sing, but that's a different, and more specific, tradition - I think.)

John