ARP requests do go out when I attempted to ping the problematic devices. This was seen with a Wireshark session running alongside the ping scanner. I found that I could not reproduce the "missing devices" I was seeing earlier that led me to ask my original question.
So, to answer my own question: ARP requests are sent per IP address when doing a simple ping scan on my subnet. I would see the ARP request go out (using Wireshark) as well as the ping request. If you need to generate an ARP request, simply send out a ping.
Even if the "problematic" device won't respond to ping requests, the ARP table will be notified of its existence.