The 802.11 standard does not require the "Distribution System" (DS)—that is, the backhaul connections between the APs—of an ESS to be an Ethernet, nor does it require the APs of an ESS to just bridge between wireless clients and the DS.
So, yes, you can set it up this way, but there are some things to keep in mind if you want to do this:
- Routers block most service discovery protocols, so you'll often discover that devices on one AP can't see clients on another AP, since the APs effectively blocking the discovery protocols.
- Most so-called "Wi-Fi routers" are not plain IP forwarding routers but NAT (technically what the IETF calls NAPT, or what Cisco calls PAT) gateways, and NAPT gateways by their nature end up blocking any connections from being originated from their "public" side to their "private" side.
- Routers (and NAPT gateways) require different IP subnets on different interfaces. If you're using a bunch of the same brand of consumer Wi-Fi routers, they're all going to default to using the same subnet on the "private" side. If you connect the WAN port on one to the LAN port on another, you'll end up with the same subnet on both sides of the downstream device. You can avoid this by changing the subnet one of them uses, or by not daisy-chaining them in this way.
- Some wireless clients might not refresh their DHCP leases when roaming from one AP to the other, so you might end up with IP address conflicts. Let's say you have two routers A and B, and both are using the same 192.168.2.x/24 subnet on their individual WLANs. If you also have two clients, X and Y, and X associates to A and gets 192.168.2.2 on A's network, and Y associates to B and gets 192.168.2.2 on B's network, and then let's say X moves away from A and toward B, and eventually roams to B. If X is well-behaved, its wireless card would have notified its host network stack of the roam event, and the host network stack's DHCP client would temporarily stop using the 192.168.2.2 address until it can reconfirm that the lease is valid on this potentially different network. But if X is poorly behaved, then X and Y will both be on B and both think they own 192.168.2.2.