Can we see the stars at the edge of the Milkyway? This question proved much more difficult to formulate than I initially imagined. It concerns how far out in the Milky Way that we actually see with different telescopes. I know the Milky Way disk is about 100k light years wide, its halo a couple of times that wide, and most of the naked eye stars are within 1000 light years. I also know that when many stars are close together they are more visible, which means we can easily see for example the double cluster in Perseus at about 7000 light years with our naked eyes. But if you take a large telescope and peer into the distance, how easily do you see through the star fields until the point where you have no more foreground stars in the field of view, and all that is there are the numerous faint galaxies lurking in the back. For example, in the Hubble Deep field you see a few stars. Are we looking at the last few stars at the edge of the Milky Way, or are there more hidden in the field that we can't see because they are too far away/too faint?

I realize that there are dust clouds in the Milky Way obscuring the view, so if you look towards the galactic center you would definitely not see all the way to the other side. But lets assume we're looking perpendicular to the galactic plane. Lets also say that you're using a 16" telescope, allowing you to see maybe down to the 15th magnitude. Do you see the stars at the edge of the galaxy?

Another way of approaching the question... From what I've read it seems we estimate the Milky Way to contain about 250 billion stars. I also read that the Gaia satellite will map about 1 billion stars. Does that mean our best telescopes are only able to discern 1/250 of the stars in the Milky Way? Of course all stars on the other side the galaxy disk are hidden from us, so they surely account for a large portion of the invisible stars. But looking straight up from the galactic plane, can we see the last galactic stars before the empty intergalactic "void"?
Take a look at the HR-diagram. You have forgotten to take into account that stars come in vastly different luminosities.  

For example, we can barely see all red dwarves out to a distance of 10pc, while we know that they vastly outnumber the more luminous stars.  

The luminous red giants however we'll be able to see on side of the edge of the disc, but even Gaia will not be able to look through to the other edge. It's limit magnitude is 20, while extinction through dust in the direction of the galactic center is often cited to be up to 100th magnitude.
Hubble deep field galaxies for comparison are around 30th mag.

However, there is Baade's window, a region just above the central galactic plane that has low dust content on our line-of-sight there. We'll be able to spy quite some stars there.

If you're interested in the Gaia mission, you can find information here.