Absolutely no doubt that you would need a very good system in place for that sort of stock profile, but I don't subscribe to the theory of keeping it small because it's easier.
Being successful in business isn't about being easy, if someone wants easy, then they don't want any great level of success, because that take a lot of work, a lot of hard work!
If it is cost effective to list in the thousands, then I would most certainly be putting processes into place to streamline it as much as possible and then test the market the with new platform. You want to make sure that you develop a good cross marketing strategy, and fine tune your store's categories for easy selection.
The one thing you DO NOT want to do is make it hard for a customer at any time whatsoever!
Once you have two or three month's worth of sales data you can sort through, that's where you will ultimately get the answer to your question and find out if it is worth the extra effort involved or not.
People can give you opinions, but good hard sales data is all that can give you real answers to a question like that!