Yes it will, but you may want to replace it with one of these:

Soy sauce – The easiest swap; use the same amount.

Tamari – Similar to soy sauce but gluten-free.

Worcestershire sauce – Has anchovies and gives a similar savory flavor.

Coconut aminos – A slightly sweeter alternative to soy sauce.

Soy sauce + a splash of lime juice – Adds the salty and tangy balance fish sauce often brings!