I don't know of any such word, and I would expect that it doesn't exist: nevermind the currency, 1000 is just not that large a number. It's only 10 times bigger than 100, so even if you've never seen 1000 of something all in big pile, you can easily imagine what it would look like - it'd be 10 piles of a 100 things.
A million, on the other hand, is so large a number that our everyday experience simply doesn't give us a good handle on it: it's a thousand thousands, and that's an awful lot of piles. Hence the desire to categorize those who hold that much wealth as something special, something worthy of its own word (i.e. apart from "wealthy").1
I think that even if you find a time, place, and currency in which 1000 represented a lot of wealth2, the number itself wouldn't be remarkable enough to warrant coining a word for it.
1An interesting side note is that in places where the currency has inflated to the point where a million is an everyday occurrence, "millionaire" still means someone wealthy: the term has become divorced from the number.
2Hint: 100 years won't do it, neither with dollars nor with pounds.