An organization has a Wireless router with MAC filtering enabled allowing only certain users to connect. If an attacker knows the password and SSID of the WLAN, and he manages to spoof one of the user's MAC address, will the attacker be able to connect at the same time while the user is connected to the WLAN?
Does MAC filtering in WLAN protect against MAC spoofing?
No, in no way.
he manages to spoof one of the user's MAC address,
You make it sound like that's a hard thing. The MAC address used by your network card is a setting in the network manager – trivial to change.
MAC addresses of other users can be observed in plain text on the air, which is trivial, too.
will the attacker be able to connect at the same time while the user is connected to the WLAN?
Yes. But that will confuse the access point, and it will probably throw both out of the network. Which makes no difference – you and the other user will instantly try to register back in.
But usually, any wireless network will be encrypted and will require the user to authenticate with his specific password (WPA2-Enterprise) or at least a pre-shared (i.e. common to all) key (WPA(2)-PSK, WEP). WEP is obsolete, but WPA2 makes it hard (brute-force hard, in fact) to enter if you don't know any password.