After Regulus Black was killed in the cave by the Inferi, did he join them and become one or just die? It seems transforming potential rivals into your own defence would have been wise, but do we know it happened?
The books don't say.
However, we do know that Regulus ended up in the water:
And Harry deduces that the point is, indeed, that ending up in the water would turn you into a defender of the Horcrux:
On the whole, I agree that it's the only thing that makes sense. The potion causes an unquenchable, irresistible thirst. The water is the only thing that will work and all who enter the water, remain in the water. And those who are in the water seem to defend the Horcrux, so I agree that yours and Harry's surmise makes a lot of sense.
It is true that there's no explicit evidence of Inferius-ification, if you see what I mean? However, that water is more than water:
We also do not know the full effects of that potion.
On the whole, I would not put it past a wizard like Voldemort to have those who end up in his lake become guardians of his soul fragment. Far from it, in fact. The entire set up seems to make little sense without that speculative component.
I also think it's very noteworthy that Voldemort makes Kreacher drink the potion and then drops the Horcrux into the basin, refills the basin, and sails away, leaving Kreacher there. His experiment is apparently complete. He sails away and leaves Kreacher to his fate, without - apparently - performing any further spells on him. Kreacher then, of course, succumbs and attempts to drink the water and gets pulled in. Job done, thinks the Dark Lord. That, apparently, is enough for him.
If more is necessary to make Kreacher a guardian, why not wait for him to die and do the magic? Well, maybe Voldemort never much fancied a House-Elf guardian and always intended him - and any other entrants to that cave - to lie silently at the bottom of the lake, with only the original Inferi as guardians. Maybe. But it all seems convoluted and pointless, if so. If so, why not just fill the basin with slow-acting poison? For sure, Dumbledore suggests that the Inferi and the darkness are there for the fear factor, as much as anything else. And it certainly seems that Voldemort wanted a potion defence that one could drink, allowing him to retrieve the Horcrux if necessary, but that would be disabling. But without the - oh and it makes you a guardian too - component, where's it really going? Why not just have it kill you outright? Why have it make you join the legions of the dead in the water?
However, the strict answer to your question is no, we do not know.
This seems to imply that Inferius is created by a conscious effort of the wizard (casting a spell).
And we know that Voldemort most assuredly was NOT aware of Regulus's visit to the cave, as he didn't know that the Horcrux went missing till he visited the cave again in Deathly Hallows.
So there was nobody to turn Regulus into Inferius.
So the answer is "NO"
Having said that, purely theoretically, wizards can leave spells that hang on a trigger (e.g., cursed objects start the curse on anyone who touches them; or alarm spell triggered by Harry in front of Aberforth's pub in DH; or for that matter Taboo spell created by Voldemort); so presumably there's an off chance that Voldemort left a "Turn any intruder into Inferius" spell in the cave which triggers if anyone is killed there. However, there's precisely zero support in canon that such a thing has happened, so I'll reject that theory as extremely unlikely.