Simultaneous Wifi Connections?

Is it possible to connect to two wifi access points simultaneously?
For example, I have WAP1 connected to 192.168.m.1 and WAP2 connected to 192.168.n.1.
WAP1 is a standard wifi network with a default route to the internet.
WAP2 is a local network with it a server at 192.168.n.1 but no route to other networks.

Yes, it is possible. But there are some requirements. The most important one, both Wifi network musst use the same channel. If there are on different channels, you need two Wifi adapter in your system.
Your network adapter and the driver need to support it. Most of them do, but not all. The driver is usually the problem.
I’m not completely sure, but NM might not able to set it up. You probably need to do it manually via the command line. But maybe NM has improved in recent versions.
If you have two Wifi adapter, like a USB Wifi adapter and a internal one, there is no problem to set it up.