Doing some more digging, from the 'Show IP statistics' command is this the amount of max concurrent connections the box has seen. (in BOLD and RED text below)
lamsdc1cs003> show ip statistics
IP Statistics - SP Slot 1, Subslot 1:
UDP Statistics:
Input Datagrams: 81,467,201 Output Datagrams: 81,467,201
No Port Errors: 0 Input Errors: 104,620
IP Fragments: 110
TCP Statistics:
Retransmit Algorithm other Min Retransmit Time: 500
Max Retransmit Time: 15,000 Max TCP Connections: 32,768
Active Opens: 302,647,530 Passive Opens: 2,831,374,249
Failed Attempts: 49,337,843 Resets: 966,887,218
Established Conns: 2,392,842,101 Input Segments: 1,112,029,840
Output Segments: 2,452,796,476 Retransmit Segments: 208,657
Input Errors: 69,601 Output Resets: 29,953,594
IP Fragments: 40,642 VIP Unavail Reset: 0