glReadPixels from a RenderTexture

I call it in update but you should be able to call it in any function. Though you won't always get data back immediately so you should not try to read into a function's local variables. All I did to test it was download the native plugin example and modify the SetTextureFromUnity and OnRenderEvent functions and add a ReadPixels function (and delete the code for API's other than OpenGL, etc.) which should make it easy to replicate.

This is the SetTextureFromUnity from RenderingPlugin.cpp

 // --------------------------------------------------------------------------
 // SetTextureFromUnity, an example function we export which is called by one of the scripts.
 static void* g_DataHandle = 0;
 static int   g_TextureWidth  = 0;
 static int   g_TextureHeight = 0;
 
 extern "C" void UNITY_INTERFACE_EXPORT UNITY_INTERFACE_API SetTextureFromUnity(void* dataHandle, int w, int h)
 {
     
     g_DataHandle = dataHandle;
     g_TextureWidth = w;
     g_TextureHeight = h;
     
 }

This is the OnRenderEvent from RenderingPlugin.cpp

 static void UNITY_INTERFACE_API OnRenderEvent(int eventID)
 {
     // Unknown / unsupported graphics device type? Do nothing
     if (s_CurrentAPI == NULL)
         return;
 
     s_CurrentAPI->ReadPixels(g_DataHandle, g_TextureWidth, g_TextureHeight);
     
 }

This is the actual read pixels in RenderAPI_OpenGLCoreES.cpp

 void RenderAPI_OpenGLCoreES::ReadPixels(void* data, int textureWidth, int textureHeight)
 {
     
     int currentFBORead;
     int currentFBOWrite;
     glGetIntegerv(GL_READ_FRAMEBUFFER_BINDING, &currentFBORead);
     glGetIntegerv(GL_DRAW_FRAMEBUFFER_BINDING, &currentFBOWrite);
     
     glBindFramebuffer(GL_READ_FRAMEBUFFER, currentFBOWrite);
 
     glReadPixels(0, 0, textureWidth, textureHeight, GL_RGBA, GL_FLOAT, data);
     
     glBindFramebuffer(GL_READ_FRAMEBUFFER, currentFBORead);
     
 //    *You can uncomment this and pass in a pointer to a texture2D "textureHandle" and copy data directly into it here*
     
 //    GLuint texResult = (GLuint)(size_t)(textureHandle);
 //    glBindTexture(GL_TEXTURE_2D, texResult);
 //    glTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, textureWidth, textureHeight, GL_RGBA, GL_FLOAT, data);
     
 }

I don't know if you can directly read to a Unity Texture2D so I added code that will copy the data (float array) to it.

My test Unity script.

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using System.Runtime.InteropServices;
 using System;
 
 public class Test : MonoBehaviour {
 
     [DllImport("RenderingPlugin")]
     private static extern void SetTextureFromUnity(float[] data, int w, int h);
     [DllImport("RenderingPlugin")]
     private static extern IntPtr GetRenderEventFunc();
 
     public RenderTexture rTex;
     public Texture2D tex;
 
     float[] data = new float[0];
     int size = 1024;
 
     // Use this for initialization
     void Start () {
 
         tex = new Texture2D (size, size, TextureFormat.RGBAFloat, false);
         tex.Apply ();
         rTex = new RenderTexture (size, size, 0, RenderTextureFormat.ARGBFloat);
 
         data = new float[size * size * 4];
             
     }
     
     // Update is called once per frame
     void Update () {
 
         ReadBack ();
 
     }
 
     void ReadBack () {
 
         RenderTexture.active = rTex;
         SetTextureFromUnity (data, size, size);
         GL.IssuePluginEvent (GetRenderEventFunc (), 1);

         Color[] colors = new Color[data.Length/4];
         for (int i = 0; i < data.Length; i+=4) {
 
             colors [i/4] = new Color (data [i], data [i + 1], data [i + 2], data [i + 3]);
 
         }
 
         tex.SetPixels (colors);
         tex.Apply ();
 
     }
 
     void OnGUI () {
 
         GUI.DrawTexture (new Rect (Vector2.zero, Vector2.one * size), rTex);
         GUI.DrawTexture (new Rect (Vector2.right*size, Vector2.one * size), tex);
 
     }
 
     void OnRenderImage(RenderTexture src, RenderTexture dest) {
 
         Graphics.Blit (src, rTex);
         Graphics.Blit(src, dest);
 
     }
         
 }

Although I'm basically only reading the framebuffer here you can invert the colors of rTex (or use a different renderTexture, etc.) to see that it is actually reading from the one set to active in ReadBack(). Also there's code in there that turns the data array into a texture but this is just to show that it works.