The question posed is problematic to answer as the traffic load is an unknown as is the traffic load destined for the Internet. However, let's ask it in a different manner - Is there any harm in tagging for QoS?
First, QoS is typically implemented whenever the impacted device is reaching saturation. When the device approaches saturation, it will begin to spawn the QoS queues in an effort to maintain the packet delivery of those with higher levels at the expense of lower tagged packets, even if it means that it has to drop some lower level packets.
So, if your network and Internet connection are adequate at all times to handle the load, then QoS will buy you nothing. On the other hand, as your switches do not support QoS, and assuming your router does, then it may be a question of if there is a need to have QoS implemented such that as packets arrive at the router and should there be the possibility that saturation might come about, would you not want the router to at least prioritize the voice packets to the WAN as best it could? You are correct in that once the packets reach the Internet (as it currently stands with net neutrality) that all packets are peer, but the delivery to the Internet as your packets traverse your firewall is still under your control.
So, the bottom line is that if all is fine now and there is no concern about congestion in the future, then there is no need. It only adds additional data for the tagging that will never be acted upon. If there is any hint of congestion, then presumably it will get worse as your needs grow, so QoS will not hurt and it may save you from future issues.