Yes, the two IP’s 126.96.36.199 and 172.16.31.19 would be in the same subnet. You could also setup 192.168.x.x with a 255.255.255.254.0 address and achieve the same result, as the 192.168.x.x range is a 16 bit subnet mask. This may be less headache since you’re used to the address space already. Change all of your subnet masks to reflect the new one and add new hosts in the second address range you choose to migrate the network.
Just realize that the reason to avoid making such a large subnet is because of broadcast storms that may be experienced with that many hosts in the same collision domain. Every system that receives a broadcast message must process the message, regardless of whether it is addressed for that machine or not. That is the reason that most people subnet their networks, not because they want to make it more complex. IPv6 is supposed to fix the broadcast storm problem by using multicast addresses versus using ARP to announce layer 2 addresses and find other computers.