I'm playing around with Modbus for an embedded system (I've never had to deal with this before) and I know that Modbus Slaves recieve an address ranging from 1-247 but does a Modbus Master also recieve an ID?
If so, is it relevant to know the Modbus Master ID when communicating?
The Modbus master does not need an address. This is explictly stated in the Modbus specs. The unit addresses that are written to the Modbus messages are slave addresses, in both requests and responses.
It is easy to see why the master don't require an address. Although Modbus RTU runs over a multidrop network, it allows only one master. The slaves are queried by the master. The master is aware that it requested data to a slave. After the required silence in the line, the slave will send the response to the master, which is aware that this response is destined to itself, because there is no other master querying the slaves.