No, it isn't, on both counts.

First, NAT is not necessarily stateful, just the common home router PAT or the telco CGNAT varieties of NAT are.

Second, NAT does not filter, that is what a firewall does. NAT only rewrites addresses. If there is no state for a connection in a stateful NAT, it looks up whether there are any rules for how to rewrite that connection, then adds a NAT state entry that specifies how to rewrite that connection (including, potentially, not at all), and in any case the (potentially rewritten) then gets forwarded--unless a firewall drops it.