Does the router support PXE by default?

Question

linux

dhcp is on the local network, but the tftp server with the system boot files is on another network behind several routers. Is it possible to transfer the default router so that the server can boot in this way?
for some reason this does not work for me, tftp timeout
shared-network test {
allow bootp;
subnet 10.14.22.0 netmask 255.255.254.0 {
option routers 10.14.23.254;
option tftp-server-name "94.151.11.23";
next-server 94.151.11.23;
}
}

Answer 1

Umm. Several routers with nats???

Answer 2

PXE is not. PXE only supports remote boot and nothing else.
And here dhcp the client - yes supports.