While this is an interresting idea (and one which others have brought up on this site before, but I'm glad someone finally turned this into a proper question), I think it contradicts both the movie's plot and its overall themes. So no, I don't think there is much evidence in favor of this theory, but there is IMHO very well evidence against it, even if not so hard an evidence (and interpretation is still a free good).
As you yourself stated in your question, Borden and his twin both lived half a life for their entire life. And in turn this is "their real trick and shows true dedication to their art". This is what actually distinguishes Borden from Angier, who always tried to go the easy way and couldn't even imagine to devote his entire life to "just a magic trick". That is why Angier doesn't get behind the old Chinese magician's trick and Borden immediately realizes it, because the old Chinese also devoted his entire non-stage life to keeping up the actual trick, like Borden did. And this is also the reason why Angier cannot believe Borden to just use a double for his Transported Man, since his own attempts with a double were not that fruitful and didn't work that well in the end, since he just wanted to do it the fast and easy way. So he thought there must be more to it than such a simple secret, but "it's the trick that impresses the people, the secret doesn't impress anyone" (which might in the end even be the reason why you yourself think there to be more to Borden's trick, he achieved to deceive even you ;)).
So given this major theme of dedicating his whole life to his art in contrast to going the fast and easy way to just to do a good show, Borden also using a cloning machine wouldn't really fit that well. And in the end Tesla himself said he never built such a thing, and while we might not believe him, he didn't have so much reason to lie at this point, I think. And even more important, what would be the reason for Borden to send Angier to Tesla if he knew he could build such a thing, since it was always planned as a distraction for Angier? While the coincidence might strike you as too coincidental, Borden sending him to the actual goal and just pretending it to be a wild goose chase would be much more of a plot-inconsistency. This also doesn't fit to Borden's reaction on this whole setup. He was as surprised as you and me that Angier actually "survived" the supposed murder, so he had aboslutely no idea that Angier had a machine for cloning himself, which wouldn't be the case had he known that Tesla could construct such a device.
So that being said let's take a look at Tesla's significance as keyword and the supposed coincidence. There is still a reason for Tesla being used as keyword while coincidentally being able to build that machine, even if not as impressive a reason. In the movie he once was at a science fair or something similar in London, which both Angier and Borden attended as spectators. Borden might very well have seen Angier there and might have seen that Angier was impressed by Tesla's rather innovative science (that might have seemed like magic at that time), while all the others literally ran away in fear. So he thought Tesla might be someone that Angier could really believe to have built such a "magic" machine, which made him a reasonable keyword, given that he lived so far away.
The fact that Tesla could in the end really build such a thing was a coincidence Borden did not anticipate, and was actually an hommage to Tesla's genius, I think. While not being an expert in this topic I know that even the real Nicola Tesla has a reputation for being quite an innovative person who had ideas that didn't get the respect or appreciation they deserved at their time (even if a duplication machine was maybe a bit over the top even for him), which also fits to his mythical introduction in the movie and his overall impressing presence (amazingly incarnated by noone else than David Bowie). So if anyone could have built such a machine at this time it would be Tesla and Borden might have been aware of this fact (even if he underestimated him and didn't really deem it possible) and assumed that Angier thought the same. So the writer of the script or book (if he was in the book, don't know) payed his tribute to the real Nicola Tesla by letting him achieve true scientific magic in the movie/novel, while presenting quite a surprising, well yeah, coincidence to the audience. It wasn't so much a coincidence more than Borden and all of us just underestimating the genius of Nicola Tesla, like real history also did.