It will achieve almost nothing - except making you a bit less wealthy.
Serving files over a network, especially in a small SOHO network with very few users, does not require a great deal of RAM - practically anything can do it. Twenty-five years ago, Windows computers with only a few megabytes or RAM (let alone gigabytes) could serve files quite happily.
It's a bit of a circular argument, but the main reason for installing more RAM is because you intend to run an application that needs more RAM, (or didn't have enough in the first place.) For example, virtual machines eat RAM for breakfast.
If you prefer some anecdotal reportage, (albeit on a different platform,) I upgraded my HP microserver from 2GB to 16GB and it didn't make the slightest bit of difference.