Touch screen & stylus compatibility?

If I connect the following touch screen monitor: 

Dell 24” FHD GTG Touchscreen Monitor (P2418HT) 

to my:

Inspiron 15 2in1 7573 (with the active pen enabled sticker on it),

then would the Dell active stylus PN338M ( rated compatible with the Inspiron 15 7000 (7573) ) work on BOTH my new monitor and laptop screen?