What type of serial communication are you using? RS232, RS485, RS422, I2C, SPI, ETC?
The type you are using will determine whether it's physically possible to have multiple masters/slaves on the same connection.
If you're using a compatible serial connection, yes... LabVIEW can do what you're asking.
As far as how... there are already lots of examples built into LabVIEW and on the internet.