From a story perspective, I've always assumed that the D&D gods still formed into rough psuedo-pantheons that had quite a bit of overlap of worshipers -- more like overlapping circles of friends than clubs with secret handshakes. Still, a lost little beetle isn't likely to be part of any of those circles and might cause some rub. I'd be hesitant to allow the cleric to split his attention/worship. Also, pity is far, far different from worship and not likely to be welcomed.
Still, if the Cleric's original god has a compatible sphere of influence, it's possible the beetle god could be seen as a long lost ally and the association welcomed. So, if the Cleric is currently worshiping a god of nature, say, and the beetle represents the cycle of decay and rebirth, then all is good. If the Cleric is worshiping a god of the sun, though, and the beetle is patron to those who toil unseen, there could be a problem. But, the way D&D Cleric mechanics work, maybe the god doesn't get as much say in the hobbies of their worshipers as one might expect.
If you do decide to allow it, I really like the Magic Initiate idea.