Out of interest, what do you mean by bot net ?
Is it a malicious server / trojan that receives a command, and then could cause trouble to other machines, maybe acting as a client sending spam mail through a mail server that lets anybody in ?
If it is indeed a server that receives a command, then a NAT router would prevent it from receiving an incoming connection.
I see if it's a malicious client program, then a NAT router wouldn't stop that.
There a alot of malicious server programs around though e.g. malicious smtp servers. Other comps then connect to the compromised one send spam through it. The user at the compromised machine then gets contacted by his ISP saying 'stop it or your get DCed/disconnected'. A NAT router stops that other users getting attacked, and in the process, stops that poor user from getting an email threat from his ISP.