Is it bad practice to have a constructor function return a Promise?

Yes, it is a bad practise. A constructor should return an instance of its class, nothing else. It would mess up the new operator and inheritance otherwise.

Moreover, a constructor should only create and initialize a new instance. It should set up data structures and all instance-specific properties, but not execute any tasks. It should be a pure function without side effects if possible, with all the benefits that has.

What if I want to execute things from my constructor?

That should go in a method of your class. You want to mutate global state? Then call that procedure explicitly, not as a side effect of generating an object. This call can go right after the instantiation:

var engine = new Engine()
engine.displayPosts();

If that task is asynchronous, you can now easily return a promise for its results from the method, to easily wait until it is finished.
I would however not recommend this pattern when the method (asynchronously) mutates the instance and other methods depend on that, as that would lead to them being required to wait (become async even if they’re actually synchronous) and you’d quickly have some internal queue management going on. Do not code instances to exist but be actually unusable.

What if I want to load data into my instance asynchronously?

Ask yourself: Do you actually need the instance without the data? Could you use it somehow?

If the answer to that is No, then you should not create it before you have the data. Make the data ifself a parameter to your constructor, instead of telling the constructor how to fetch the data (or passing a promise for the data).

Then, use a static method to load the data, from which you return a promise. Then chain a call that wraps the data in a new instance on that:

Engine.load({path: '/path/to/posts'}).then(function(posts) {
    new Engine(posts).displayPosts();
});

This allows much greater flexibility in the ways to acquire the data, and simplifies the constructor a lot. Similarly, you might write static factory functions that return promises for Engine instances:

Engine.fromPosts = function(options) {
    return ajax(options.path).then(Engine.parsePosts).then(function(posts) {
        return new Engine(posts, options);
    });
};

…

Engine.fromPosts({path: '/path/to/posts'}).then(function(engine) {
    engine.registerWith(framework).then(function(framePage) {
        engine.showPostsOn(framePage);
    });
});