Yes! W5200 has 8 sockets used at the same time with each 2k memory.
It means you can open two sockets as SNMP and Webserver.
There are each 16k memory in each TX and RX.
And you can handle the memory size as much as you want from 2K to 16K.
But as you understand, if you open socket0 with 16K, it means you cannot open socket anymore. (there is no more memory)
About SNMP and Webserver, we do not have performance issue. It is ok to open two sockets as ANMP and Webserver.
If I find any issues about it, I will let you know.