When I initially started reading you post I though that each quad used a different texture (since you stated "Before drawing each sprite, I'll bind its texture") but then you said that each sprite has "the same texture".
A possible easy win is to control the way you bind your textures during the draw since each call is a burden for the OpenGL driver. If (and I am not really sure abut this from your post) you use different textures, I suggest to go for a simple texture atlas where all the sprites are inside a single picture (preferably a power of 2 texture with mipmapping) and then you take the piece of the texture you need in the fragment using texture coordinates (this is the reason they exist in the end)
If the position of the sprites change over time (of course it does) at each frame, a possible advantage would be to pack the new vertex coordinates of your sprites at each frame and draw directly from memory (possibly over VAO. VBO could cost more since you need to build it each frame? to be tested in real scenario). This would be a good call pack operation and I am pretty sure it will bust the performances.
Consider that the VAO option could be feasible since we are talking about very small amount of data and the memory bandwidth should not represent a real bottleneck (each quad I guess uses 12 floats for vertex coordinates, 8 for textures and 12 for normals, 128 byte?), it shouldn't be a big problem over VAO.
About opacity, can't you play using an uniform to your fragment shader where you play with alpha? Am I wrong with it? It should work.
I hope this helps.
Ciao, Maurizio