Not both at the same time, unless you have a multi-port HomePlug or use a small cheap Ethernet switch (eg TP-Link) which will need an extra power point for its wall-wart.
Don't fall for the Ethernet cable splitter, all that does is use the redundant cores in an 8-way cable (only 4 are used normally) to make two connections over one cable and still needs de-muxing and two ports at the other end.