No. Routing decisions are made on a best match basis, this being the smallest subnet within which the target address falls.
For the rules given any destination included in 0.0.0.0/24 will be forwarded to 0.0.0.0, similarly 192.168.10.0/24 to 192.168.10.1, then anything else to 0.0.0.1.
Aren't we at cross purposes, these are DHCP networks not routes? He currently has ..
/ip dhcp-server network
add address=0.0.0.0/24 gateway=0.0.0.0 netmask=24
add gateway=0.0.0.1
add address=192.168.10.0/24 gateway=192.168.10.1
Of which the first and second look meaningless and should be removed.
Which would leave the relevant bits of DHCP server configuration as ...
/ip pool
add name=dhcp_pool10 ranges=192.168.10.2-192.168.10.254
/ip dhcp-server
add address-pool=dhcp_pool10 disabled=no interface=ether2 name=dhcp1
/ip dhcp-server network
add address=192.168.10.0/24 gateway=192.168.10.1
And I think that should work, dishing out addresses from the 192.168.20.x subnet via ether2, and giving the router's own address as default gateway of 192.168.10.1
Whether it will work as a router of not is a different matter and depends on other interfaces, rules, NAT etc.