St. Phillip is a deacon, and is depicted without a beard.
St. Lawrence is a deacon, and is depicted with an incipient beard.
St. Vincent, Deacon-Martyr of Zaragoza in Spain is depicted without a beard.
St. Stephen is a deacon and is depicted without a beard.
St. Romanos the Melodian, a deacon, does not have a beard
St. Euplus is a deacon and has no beard.
St. Rufinus is a deacon and has no beard.
St. Benjamin is a deacon and has an incipient beard.
St. Aeithalas is a deacon and has no beard.
St. Cyril is a deacon and has no beard.
St. Timothy became a bishop and all bishops have beards.
From this brief survey it would seem that the beard itself is not a symbol of the full priesthood (or episcopacy for that matter) but rather of their youth. If it were such a symbol Sts. Lawrence and Benjamin would not be given beards. There are many things in iconography that are highly symbolic, such as having a very long beard on saints who lived to a great age. However, it does not seem that there is anything which precludes icons of deacons from having a beard if said deacon actually had a beard while alive. That being said, when I looked up icons of deacons in "The Painter's Manual of Dionysius of Fourna" (THE authority on how to paint icons) of the eight deacons listed 6 do not have beards and the two listed with beards have their beards described as incipient. Incipient means "beginning to come into being or to become apparent." Thus the beard is more a sign of age-in this case youth-than priesthood. This study seems to give the understanding that atleast in the early church deacons were quite often very young men while bishops-who often have beards that go down to their waists-were mostly very old men.
I hope I have helped you.