I expect with a suitable build and configuration it can be; its earlier version (still known as “LoRaServer”) runs on the tiny little MT7628 chips having a fraction of the memory in the “industrial” gateways). Also Chirpstack’s own pi image explicitly lists the pi zero W as a target: https://www.chirpstack.io/gateway-os/ (and in fact the RAK7246 specifically is listed as a supported target of the sd card image; they refer to it as the 2246 but link to the 7246 product page)
Computation wise, it would have to be a terrible inefficient implementation for the load of handling the amount of traffic a gateway’s radio can actually pull off the air to start to be a problem. And not having the network latency of exchanging information with an external server would likely counterbalance the degree to which the processor in the gateway is more limited than the sort of cloud instance that would traditionally run a server.
That said, there are two major concerns when running any network server on any gateway itself, rather than in the cloud:
You can really only have one gateway in the network, since most gateways are connected to the Internet by schemes that don’t have much support for peer-to-peer traffic as would be needed for one gateway to report to a network server physically contained in another
If something happens to the gateway or its filesystem (corrupted, failed, struck by lightening, lost, stolen) then unless backed up elsewhere, all of the node session address/key records will also be lost, which means you can’t simply replace the gateway and have things immediately start working again, but need to restore all the session details or wait for the nodes to register new sessions with the new server.
My take is that if the network server is already installed in the box, then it’s perhaps a useful introduction or demo. But really by the time use for any actual purpose is contemplated one should be pointing the gateway(s) at a network server in the cloud - be that any of hosted chirpstack, chirpstack on one’s own cloud instance, TTN, or something else.