Only under very specific (ideal) condition. It depends on many factors, starting from the calibration, the combination of element, the acceleration voltage, the applied correction function, but also the sample homogeneity, preparation etc. For a rough shot it is OK and this is usually for many questions sufficient. You need to consider that nowadays all system work with approximation models (standardless). For more reliable measurements you need to use standard-related procedures. All system have this options but it definitely represents a (good) compromise. 

Similar problems also appear in case of an electron micro probe (WDX). High precision but the accuracy can be quite bad. For EDX it is in fact vice versa, accuracy acceptable, precision much worse than WDX. 

Other artifacts are sum peak, escape peak, non-planar surface (signal comes from somewhere else), sample contamination (to prevent charging), variable pressure mode, instability of the sample in vacuum or under the electron beam... The list is long so that the chance to make errors is quite high, especially if you are dealing continuously with other materials.  

I agree with you@Gert Noize. But what about the accuracy of EDS (Energy Dispersive Spectroscopy) when compared to standard chemical methods to find elemental composition.

Is the accuracy (or efficiency) enough to carry out the experiment to find the elemental composition using EDS for SEM (Scanning Electron Microscope)?

If the accuracy is not acceptable for EDS, what are the methods suitable to find the elemental composition?

It is not the original problem of EDS but mainly experimental errors as for chemical analysis as well. In fact YOU are the most critical component... The results are correct (if we exclude software mistakes), you only need to judge them correctly. If you find carbon in your analysis, it does not mean that carbon is inside since you perhaps measure a strong C-contamination on the surface (which can be different for different materials). If you do a chemical analysis you also have to take care that you don't contaminate your sample by residuals from former analysis. Finally no technique will give you correct data when you don't understand what is going on and which requirements have to fulfill since they are assumed in the software as restraints of the applied algorithms. Therefore, absolute values are in many cases questionable whereas relative results (precision) are often more reliable.

Thus, the answer on your question is: be critical, don't believe every number shown in a software, collect your own experiences, and read (mainly old) books since there everything is often better and more fundamentally explained than in new books where they usually only refer to older publications. Try to understand the physics behind the observed processes and try to get a feeling what statistics means and how big errors can be. If somebody tells you that the registration limit of the technique is e.g. 2%, then this is frankly speaking a lie for adults. There are combinations of elements where the reliability can be clearly better than 1%, but there are also combinations where it can reach easily 30% (like for carbon). This is not EDX-specific. The same happens even for XRD. The "2% rule" for the minimum phase fraction is only correct for two phases which are clearly different in their peak positions AND which have a very similar scattering power. Fe particles in a polymer you can even register with much lower concentration of 1%. In other words, there are some rules...but these are only rules, i.e. they are acceptable in 90% of all cases. But since you do not know whether your sample belongs to the 90% or to the 10% you actually don't know anything and you are only claiming something which has some statistical worth.