How to automatically import new songs from iTunes media folder on different devices?

I'm afraid not. It is one feature that personally I feel is sorely needed.

I keep one machine as my 'master' & every so often I port the iTunes Library.xml file across to the other machines.
In order to not make this take the entire day, there is a trick to 'break' the .itl file, which makes the import process take far less time. It does lose playlist info from the recipient machine & a few album covers always tend to go missing, but it's the best workaround I've discovered, after many years of trying.

Remove the existing .itl file from ~/Music/iTunes/ then create a new, 'broken' one from Terminal [copy the old one for safety if you prefer, but I've never found a way to manually insert data from one into another]
Open Terminal & enter this touch ~/Music/iTunes/iTunes\ Library.itl That will create an empty ITL file, broken enough for our purposes.

Next time you launch iTunes, it will see the corrupt .itl & rebuild it [it will claim to be importing]. This is very much faster than having an .itl that doesn't match what the .xml thinks it ought to be, minutes rather than hours.