There is pretty much no way that Splenda can kill your gut bacteria. I think that is based on Young's 1990 paper, but it was never widely cited (like 10 times in 20 years). LaBare has a couple of papers from the early 1990s demonstrating partial metabolism of sucralose by bacteria (e.g. different results from Young). I know there was a rat study or two supposedly showing changes in microbial community composition, but they were published by toxicologists, not microbial ecologists, so I'm kind of suspect of their results. Genomics of gut metabolomes have shown the presence of dechlorinase--e.g. the sort of enzyme you need to cleave the chlorines from sucralose and made it edible if you're a bacteria, but, as far as I'm aware, no one has followed up on this observation. Splenda has been around for a long time, so the genes necessary for turning it into food have already spread amongst human commensal bacteria in all likelihood. Which is to say, while obviously modifying dietary sugars will have an effect on microbial ecology, it is unlikely that Splenda is specifically killing "good" vs "bad" bacteria. So far as I'm aware, other than those kind of bad rat studies, no one has looked at the issue (and by no one, I mean no reputable microbiologist).
Beyond that, even if Splenda did select for different groups of commensals, I'm not sure why that would lead to constipation. Yes, there is cross-talk between microbial biofilms and the gut mucosa, but it isn't exactly clear that the Splenda selected bacteria would also decrease gut motility (thus leading to constipation).
