It was confirmed in the 2013 Christmas Special, Time of the Doctor, that The Doctor only has 12 regenerations, and that as Matt Smith he was on his final one. This confirms that the Doctor we see get shot by River Song IS infact the Teselecta mimicking a regeneration- because he wouldn't have started to regenerate if it was really him.
As the Teselecta was designed for spying and infiltration, and can even replicate a motorbike, it's likely it's design could allow it to emit light to create the effect of a regeneration.
Even if the original design didn't allow that, the Doctor was there to lash something up that would do the job.
I was looking at a comments page and someone had typed that they had noticed a slight difference between when the Doctor was shot in "The Impossible Astronaut" and "The Wedding of River Song". This suggests that in "The Impossible Astronaut" we saw the real Doctor die and attempt a regeneration. But in "The Wedding of River Song", it could just be the teselecta falling down dead and River Song telling Amy and Rory the Doctor was dead without saying about the regeneration. They burnt his body afterwards, so everyone apart from the Doctor, his companions and the crew of the teselecta would think he was gone for good. If this were the case, then Steven Moffat never actually lied in the interviews about it being the real doctor dying in "The Impossible Astronaut".
I think that it was able to mimic biological functions, such as the faint in "Let's Kill Hitler"