As @MarkBaker said, there are lots of "accidental" rhymes in prose that no one notices. But if you structure your prose to call attention to a rhyme, I think in practice it's not prose any more, it's poetry. Maybe a very short snippet of poetry, but poetry. Or at least, I think that's how the reader will perceive it.
So the question becomes, When is it appropriate to include poetry in your story? To which the answer would be, If it's the sort of thing that people write poetry about.
If two characters are describing how to repair diesel engines, and one of them lapses into poetry with no explanation, this would be very strange and probably ludicrous. (If you had just been explaining how the one character is totally fascinated by diesel engines and loves diesel engines more than he loves his wife and children and so on, it might work that he is writing poems about diesel engines. But that's a pretty far out case.)
If a man is talking about how he just met the most beautiful girl in the world and he is swept off his feet and then he makes up a couple of lines of poetry about her, it could work, if you do it well.
The example you gave ... I don't know. "Together forever" is a commonly used rhyme, you see it on jewelry and greeting cards a lot, kind of a cliche, so it might work. Or if as this guy is dying he makes up a couple of poetic lines about his girlfriend (or whatever is going on here), that could work if you do it well. I don't think your example is bad. I just don't know that it adds much.
(I am reminded of a book I read years ago, "The Blue Adept", where a character is unaware that he has acquired magic powers that are exercised by casting spells in rhyme. And so he accidentally causes strange things to happen every time he inadvertently says words that rhyme. Like one time he casually says, "It has somewhat the form of an electrical storm." I thought that was a pretty clever plot device.)