Does it make any sense or rather is it scientific to take random languages that have no prior evidence of kinship and apply the historical comparative method?
Scientific? Absolutely! At least, if you're going by one common definition of "scientific", meaning "making falsifiable hypotheses, doing experiments to gather data, rinse and repeat".
The comparative method is so useful specifically because it fits into this cycle. The way it's conventionally used, it assumes that language change is for the most part uniform and regular. So if we hypothesize a relationship between Latin initial
/p/ and German initial
/f/, the comparative method suggests that there should be quite a lot of similar-looking, similar-meaning words in Latin and German, where the Latin word starts with
/p/ and the German word starts with
/f/. If we look at the data, that's exactly what we find (and exactly what Jakob Grimm found).
Is it useful to do this? Well, that depends on your use case. If nothing else, rediscovering something like Grimm's Law can be a great way to introduce students to the comparative method and teach them how to apply it in practice. And especially outside the Indo-European family, there are a whole lot of languages whose categorization is far from certain.
And, after all, there is the chance (however remote) that you'll discover some new connection that's been overlooked in the past. But the odds are slim; remember that the null hypothesis is always that two random languages have no relationship to each other, and it takes quite a lot of evidence to reject that. Learn from the mistakes of Nostratic and Proto-World analyses, and be ready for a whole lot of failures before finding an actual connection.