Devices on a LAN learn about other devices by one of three ways:
1. They need to send a packet to that device for the first time.
2. Another device sends an ARP request to them.
3. Another device sends a gratuitous ARP.
To answer your question, yes, it is possible (and maybe likely) that devices exist on a LAN without being and a particular devices ARP cache. (Layer two switches are a good example, as they rarely need layer 3 communication to devices other than their default gateway).
If this is a layer-2 switch, then this is normal. A layer-2 switch does not participate in the layer-3 communication between servers, and so does not need the servers in its ARP cache. In fact, the only hosts that you will see in the ARP cache are the ones that have been talking directly to (as opposed to through) the switch.
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