Yes, it is a modern English word. Your sentence is fine. However, the word is not used very often. It has a formal, only an English professor would use it type of feel. I would only use it if I was extremely emotional, or trying to make a joke out of how ridiculous something was.

Yes, it's a modern English word. No, it isn't used very often. Although it is part of current English, it has a high "register;" it sounds formal and "literary." As a check on current degree of usage, I like to do searches on Google News, because newspaper are written in good English, but are not trying to use language in a sophisticated or eloquent way. I quickly find these. (Significantly, I found a number of them in sports reporting.) "Trump's preposterous bin Laden comments" "Tom Kuhnhackl scored a preposterous goal backhand goal while flat on his back. Uh, well, this was insanely lucky." "Gwyneth Paltrow’s preposterous gift for that tricky-to-buy-for person"

'modern' is a bit ambiguous. Did you mean 'is it in current use', or 'is it a recently invented word'? I assumed you meant 'recently invented', but the answerers obviously interpreted it as 'current'. To clarify. It is current used, but not recently invented, and it was much more common a few hundred years ago, which is why it has an older feel to it.