If I accelerate through space, can I say all stars gain kinetic energy? Suppose I accelerate through empty space. Say all stars are small heavy marbles I can use to do work with by means of their velocity. Say I can let them smash into some generator that turns their motion in electricity.
Will the maximum energy I can gain be just my own kinetic energy wrt to these marbles? If so, does it make sense for me to say that there is a huge amount of kinetic energy residing in the marbles?
Let me make myself clearer, as some people don't seem to get what I mean.  An accelerated frame in empty space is equivalent to a non-moving frame in a gravity field. On Earth I can gather all marbles that fall down on Earth and turn their motion into electricity, if I want. This can't be done, obviously, in an accelerated frame. Maybe if an Earth-sized object accelerated along. Which would cost more energy than I would gain from collecting the marbles. So, even if all marbles have kinetic energy in my frame, accelerating through space, I can't collect it. Then in what sense they have kinetic energy?
 A: No.  You don't get to change the frame of reference you are using for consideration as a way to create energy.  It doesn't work anyway.
Just because some object has a lot of KE in one frame doesn't mean that the energy is available.  In order to extract it you have to interact with it somehow (in this case, that is your generator that they smash into.
It is only the relative motion between the marbles and the generator that matters.  By modifying your frame of reference, you change the KE of both, but you do not change the relative velocity.
Imagine watching a car crash from an airliner.  The car appears to be driving 500mph!  But when it crashes, it only slows to 480mph.  The energy released from that deceleration is small.
A: 
Will the maximum energy I can gain be just my own kinetic energy wrt to these marbles?

No, your own KE will not be the limit.
The marbles can exchange momentum and energy, and energy can change forms between kinetic and other forms of energy. The minimum KE will be achieved when all of the marbles are at rest with respect to the center of momentum. The amount of energy thus converted from KE to other forms will not generally have anything to do with your own KE.

If so, does it make sense for me to say that there is a huge amount of kinetic energy residing in the marbles?

Yes. Whether the energy can be extracted or not is not particularly relevant. In the reference frame you describe there is a potential energy, and for conservation of energy the potential energy lost by the marbles must be balanced by kinetic energy gained. You cannot dismiss the KE without breaking the conservation of energy in that frame.
A: That's an interesting question, in that it hinges on what you mean by the word 'gain'.
Suppose you and a trillion 1kg marbles are all at rest relative to each other. Your collective KE is zero.
If you start moving at 10 metres per second, the KE of the marbles in your new frame is 50,000,000,000,000 joules, so you might conclude they had 'gained' extra KE.
However, the marbles have not gained that KE as a consequence of your acceleration. Before you started to move, the marbles already had a KE of 50,000,000,000,000 joules in that frame.
The point is that KE is frame dependent, so you can make the KE of the marbles take any value by picking some reference frame to quantify it in.
In that sense, the value of the KE is meaningless. To transfer the KE of the marbles (ie to use it to do work), the marbles need to interact with something. Suppose that when you accelerated to 10m/s you were carrying a generator that consisted of something like a waterwheel, so that as the marbles passed you they collided with the paddles and caused the wheel to turn. Each collision with a marble will slow you somewhat, so that after a number of collisions you will eventually end up at rest with the marbles again (ie in the frame in which they have zero KE).
By conservation of energy, the maximum energy you could extract from your marble-wheel generator would be equal to the energy you had expended in accelerating it and you to 10m/s.
