hardwire printing from iPad to USB laser printer

unless the brother printer explicitly state this is supported I would say no

when one install a printer on a computer one install a driver a piece of software made by the printer manufacturer enabling the computer to talk with the printer sometimes the send their drivers of existing printers to be bundled with the macOS this is not a system used in iOS

with ios devices apple made a generic printing interface called airprint About AirPrint - Apple Support

that printer manufacturers can choose to support I believe this to be only supported over wifi.

AirPrint as a network protocol (actually it uses a several IP Network Protocols) doesn’t care whether the network is WiFi or wired Ethernet. The protocols themselves are all IP-based; as such, an AirPrint print-server installed on a wired network segment will work quite happily.

However, most consumer-grade AirPrint printers, featuring multiple interfaces (e.g. have a single WiFi network interface plus a USB interface - or feature multiple network interfaces such as WiFi plus a wired Ethernet port), generally only implement AirPrint on the WiFi network interface. In such cases, the printer must connect to the network via WiFi for AirPrint to function.

So, to accurately answer your question

a) Where AirPrint is explicitly supported by your your printer or connected print server over its wired Ethernet port - you are theoretically able to print from your iPad to AirPrint enabled devices connected to your wired Ethernet network segment.

b) Many printers only support AirPrint over their WiFi network - and it may not be possible to directly print from your iPad.

In summary, AirPrint is IP-based, but its implementation on a specific network interface is at the behest of the printer manufacturer.

I hope this clarification is helpful in resolving the question.

Is your printer's model number DCP-L2500D or a different model? If so, which?