While I know that such a switch switches TCPIP packets so your old internet VOIP is fine there are VOIP telephones that require other hardware.
Until you detail out what differs from your VOIP phones and just internetIP packets I'm going with "Yes, it works."
Does this switch support IP Phones? I believe only PoE switches do. I ask because a vendor sold one of my customer a bunch of these switches and told her that they do support VoIP.