One possible solution would be to create a canvas element using the 'selector' class|id to style it. 
Then you could establish the RGBA of a pixel on that canvas.. VERY 'hacky' but its the only thing my little brain can think of! 
Something like this (Not tested!): 
Lets say your html looks something like this :
    
<style>
.background_element{
background:linear-gradient(to right, #fff 87%,rgba(238,237,233,0) 100%);
}
</style>
Then you want to check the background colour .. so we create a canvas object to clone the div at that time. 
var canvas = document.createElement('canvas');
//apply width and heigh 1px
canvas.css('background-color', $('.background_element').style.backgroundColor);
Then we cant to get the colour of a pixel on this canvas.. 
var pixelData = this.canvas.getContext('2d').getImageData(1, 1, 1, 1).data;
console.log('R: ' + pixelData[0] + '<br>G: ' + pixelData[1] + '<br>B: ' + pixelData[2] + '<br>A: ' + pixelData[3]);
This would log the RGBA to the console.. Maybe.. 
- Note: I dont recommend this for production env of course, meerly a
   proof of concept!
Inspiration
Alternatively
You could be very fancy and really strip into the RGBA with HTMLelement.prototype.alpha! :) 
Something like : 
HTMLElement.prototype.alpha = function(a) {
        current_color = getComputedStyle(this).getPropertyValue("background-color");
        match = /rgba?\((\d+)\s*,\s*(\d+)\s*,\s*(\d+)\s*(,\s*\d+[\.\d+]*)*\)/g.exec(current_color)
        a = a > 1 ? (a / 100) : a;
        console.log("rgba(" + [match[1],match[2],match[3],a].join(',') +")");
      }
Again very messy but there is a good chance this will be more percise !