actually becoming more interested in others
What does this mean? How do we measure it? These are questions that need (or at least, should) to be answered before we can even begin studying this question. In this answer, I will sketch some of the difficulties in answering these questions, and argue that the state of the art in psychology/neuroscience/etc. is not capable of resolving them. As such, even though cannot answer the question whether this has been studied, I argue we ought to be skeptical of the results if it has.
What's the difference?
What is the difference between being interested in another and behaving as if you do? I'm sure you tell yourself a different story if you believe you are genuinely interested in someone, rather than faking it. However, that's exactly the story I'd tell myself if I'm not interested at all, but want to fake it effectively. In fact, why do we care about what stories people tell themselves at all? These things don't seem to tell us more than the actual human behaviour, and the influence it has seems to be rather limited. Off with their heads!1
... or at least, that's what the proponents of Behaviorism would have thought of the matter. Skinner believed that, as a result of his behavioral experiments on animals, there is no need to posit the existence of any internal experience or thought in order to describe behaviour in humans and other animals. At the time (early 20th century), this seemed a reasonable restriction. After all, how on earth could we figure out what happens on the inside of the skull?
Now that we can do exactly that (with fMRI, for example), behaviorism seems less attractive. As we can now measure activation of certain brain regions not only correlated with behaviour, but also with observation, limiting yourself to behaviour seems too strong. (unless you would extend "behaviour" to include activation of brain regions, but now we're just arguing semantics)
So, let's ask again, what is the difference? Perhaps there are distinct brain states correlated with genuine interest and fake interest that nevertheless can fool others. That is an interesting hypothesis. Big, if true. I mean, if we have some sort of device that can tell us whether you're faking interest, we basically have invented a (highly specialized) lie detector. While there is some work on fMRI lie detection, the type of 'deceit' we wish to detect here seems too complex for the current techniques to capture.
How do we measure it?
You may not be convinced by my philosophical objections. Maybe that is the wrong approach, if we can measure something interesting that is close enough, then we can fix the philosophical conundrums later. One's modus tollens is another's modus ponens, after all. Fair enough. Let's try to measure anyway.
Perhaps we can measure genuine interest by testing whether the interest in the person is retained when it is no longer strategically useful. There are many problems with this idea, such as the fact that humans aren't perfectly rational, but more importantly that we are not aware of the mechanisms that produce fake interest, and their side-effects. An effective faker would employ as much of the techniques to generate actual interest as it can afford, because genuine interest is presumably a natural behaviour that has evolved to be highly effective in humans. (unless they have a severe mental deficiency, such as clinical psychopathy. But I presume we want a claim about healthy humans) This means that even the faker can show side-effects that would be strategically useless, if those side-effects are the lesser evil.
So side-effects of genuine interest are out. What else can we measure? Perhaps we could look at the side-effects of fake interest. We could test whether if person A appears interested in person B, person A would later betray person B, or not. However, this runs into the opposite problem. For an ordinary person to betray another, we would expect there has to be some incentive to do so. However, the same incentive could lead to someone with genuine interest to also opt for betrayal!
Well then, what's left? I have no clue.
As I said above, I do not know whether anyone has attempted to study this question. Still, it seems there are several fundamental problems in designing a study to answer this question, and I think it is reasonable to claim that effectively studying it is out of reach for the current state of the art.
1: With apologies to Lewis Carroll.