Hi,
First let´s try to make it clear. On thing is Syslog and other thing is MIB.
Syslog is a protocol that allows you to send device´s logs to an appropriate server, where you can monitor devices´s activities. This is very helpful when it comes to troubleshooting.
MIB (Management Information Base) is a 'database' and allows you to read information on devices using the SNMP protocol.
As per your question, Yes, there´s an MIB for NAT, "CISCO-IETF-NAT-MIB". With this MIB in your hand, you can find out which OID you need to get the information you want. Then, you can use and NMS to show this information for you.
You can download MIB here:
ftp://ftp.cisco.com/pub/mibs/supportlists/asr1000/asr1000-supportlist.html#_Supported_and_Verified
Hope that help.