Ethernet Encapsulation does not change how the serial protocol works. If the serial protocol did not allow multiple master connections before the use of the Serial-to-Ethernet converter, then it will not allow it afterwards. An Ethernet-to-Serial protocol converter is different. If the Ethernet protocol allows multiple connections, then the converter will parse the requests so that more than one master can ask for the same serial data.
For example, a Modbus Ethernet-to-Modbus-Serial converter will allow multiple Modbus Ethernet connections. It will manage the requests on the serial side, making sure that only a single serial request is on the line at once.