I think I'll revive this thread.
I have nothing to say about Hebrew, but you can certainly classify a conlang in a natural language group. That's what I've done with Tikolmian and Conilan. I like to say Tikolmian is Indo-European the same way English is Germanic. In other words, Tikolmian has a recognizably Indo-European syntax and grammar and a few cognate words, but it's been heavily influenced by a totally unrelated language, that of the Cryptian cats. At least, this is the backstory. None of that is actually true. It's based on English, but you'd never know it because I run the words through an encoding. If any of them look similar (which some do), they've been borrowed or it's a total coincidence.
Conilan is French without the main sound changes that are unique to French. I've left in the b to v change and such, but the phonology is much closer to Spanish. So it's definitely a Romance language that evolved from Latin, and might even have existed had French taken a slightly different course.
Fooblian, however, is a member of its very own imaginary language family. I haven't created any of its relatives and probably never will, though. It's a relative of the cat language that influenced Tikolmian.
Really basic: Español, lingua latīna
Conlangs (current): tikolmil, llyffws, Arliks, dilir
(Website is at http://risteq.net/
if you ever want to visit. It's supposed to be in 4 languages.)