Very likely yes.
The MicroLogix 1400 supports messaging over Ethernet to PLC-5, SLC-5/05, other MicroLogix, and ControlLogix using the "EtherNet/IP" application protocol.
The qualifier is that some older PLC-5E and 1785-ENET "sidecar" modules don't support the "EtherNet/IP" protocol, only the older PLC-5 specific "CSPv4" protocol.
See if you can determine the Series letter and firmware revision of the 1785-ENET card. Series A Rev D and later, and all Series B modules support EtherNet/IP.
As a first test, use the TCPing utility (elifulkerson.com) to see if the PLC-5 will accept a TCP Connection on Port 44818. The embedded web page on the 1785-ENET probably also lists the firmware revision.