We’ll make an assumption here and say “yes” (and we do appreciate that budgets wildly vary).
Christie’s, Philips, Sotheby’s, Antiquorum, Heritage… All the largest and most well-known houses have, virtually without exception, watches in their auctions with low estimates starting around $2,000 USD, and some without reserve (which means that the watch will sell, regardless of dollar amount, to the high bidder).
A great example of the range of prices at auction is a stainless steel Patek Phillipe 1518 that sold for over $11M USD at Phillips: The Geneva Watch Auction Four in November 2016, setting a new world record for a wristwatch.
The low estimate of the next lot? $2,000 USD.