Pinch of salt?

You'll observe that many cake and other dessert recipes call for a tiny bit of salt. Its purpose is not to make the food taste salty, but to amplify the flavors. A theory about why this works is that the sodium and chlorine ions in solution increase the conductivity of the mix in your mouth as you're chewing it, thereby sending a stronger signal to your taste buds (which are electrochemical receptors after all).

Not sure about that theory, but I do know that a smidge of salt well below the flavor threshhold improves many non-savory dishes.

Do you think it might do the same for beer? I'm talking tiny quantities, like a quarter-teaspoon per gallon.

Depends on your water supply and chemistry. A tiny bit of sodium can be ok, under a 100ppm especially in darker beers, too much especially with high levels of sulfate in the water can taste harsh. And chloride ions (usually supplied by calcium chloride) can enhance the taste of maltier beers. But regardless, you need to know your water chemistry and mash ph, etc.

+1 to knowing your water chemistry/pH and whatever.

As somebody that enjoys slinging ingredients in the kitchen (without much knowledgeable reasoning), I completely understand your reasoning about amplifying flavors by adding salt.

However, it seems to me that approach to the use of salt would mostly apply to whether or not/how much or little salt you might dash into a glass as you pour the beer. When you add it to the mash/boil/fermenter, you are messing with the water chemistry rather than doing a beer version of 'seasoning'.

I mean consider the differences in the processes. Whether cooking a turkey or baking a cake, the absolute longest time between adding salt and consuming the end product is maybe a few days at the most. But if you add salt to a beer, even if it as late as the bottling, you'll still be waiting a couple weeks before drinking it.

I don't know enough to understand why it would be different, but I have a hard time believing any salt addition would have the same effect after a couple weeks in a beer that it would have after a day or so in a cake.

Caynne pepper in very small amounts also enhances flavor, much like salt. Probably would have less impact on water chemistry.

There probably already is some salt in your water.

Get a water report from your city. It will list, among other ions, sodium (Na) and chloride (Cl) as parts per million, which happens to be equivalent to milligrams per liter. So if you already have 100ppm Na and 150ppm of Cl in your tap water, there's a little less than a teaspoon of table salt in 5 gallons of water.

Sodium, chloride, magnesium, calcium, sulfates, carbonates, and bicarbonates are typically the ions brewers care most about. In addition to having a large impact on mash pH, which is important for enzymatic action in the mash, they all enhance or detract from certain flavors much in the way that plain old salt does for food.

Just stumbled across this on CraftBeer.com Note sea salt as an ingredient.

Predicting Craft Beer Trends in 2015
By John W. Mitchell
Craft Beer Trends
For Jeremy Danner, Ambassador Brewer at Boulevard Brewing Co. in Kansas City, Mo., the variety of styles he brews is driven by a white-hot craft beer truth.

“People want to drink something interesting,” Danner says. “They want to be wowed and enjoy themselves.”

To help satisfy this expectation among Boulevard customers, in their 2014 summer lineup Danner and the Boulevard brewers turned to a 200-year-old German beer style: the gose (GO-suh).

Their interpretation of what he calls a “low-ABV sour” received a dose of coriander and sea salt during the boil before it was infused with hibiscus flowers. The resulting vibrant pink Hibiscus Gose flew out the doors during its limited release.

Yes, but it depends on what's already there in your water. Your water might have sodium and chloride in it and if you add NaCl to your brewing water, you might wind up with too much sodium.

And FWIW, last time I used NaCl in my brewing, the amount was something like a gram for the WHOLE batch. 1/4 tsp per gallon is guaranteed to be way, way, way too much.