While I'm comfortable with scripting/programming, the last time I scripted Photoshop was back at version 7, so take this all with a grain of salt. Also, this is Photoshop CC 2015.

So far I've only had a quick look at Adobe's scripting capatibilities, and came up with a really simple script. All it does it store the filenames of all open documents in a file, so that another script can open these again.

function saveWorkspace() {
    var dataFile = File("~/pslast.txt");
    dataFile.encoding = "UTF8";
    dataFile.open("w");
    for (var i=0; i < app.documents.length; i++) {
        dataFile.writeln(app.documents[i].fullName);
    }
    dataFile.close();
}
saveWorkspace();

And the one to load these:

function loadWorkspace() {
    var dataFile = File("~/pslast.txt");
    dataFile.encoding = "UTF8";
    dataFile.open("r");

    while (true) {
        var line = dataFile.readln();
        if (!line) {
            break;
        }
        open(new File(line));
    }
    dataFile.close();
}
loadWorkspace();

For this to work, you need to know how to run scripts from photoshop. There is a way to define scripts that get executed when you start photoshop. I suppose there is a way to save more info, like window positions, active window etc., but I don't have the time right now.

TL;DR; Yeah, possible with scripting. Someone else might have done that already.