It will depend on many things, like the quality of the network and the server setup (among a very large list of things).
First of all, if you want 1000 persons uploading images at the very same time you will need a lot of CPU and RAM because the PHP process of image resizing take a lot of the load. So a VPS with 2GB of ram should be OK if PHP can widely use this machine. If you limit PHP memory to 8MB then you will notice that you won't able to support that load.
Now, 1000 uploads at the very same time also means a high rate of HDD writting so the IO rate of the hard disk should be huge. You have to think about this like a computer where 1000 persons will be at the same time writing images to the disk, using memory to resize images, using a mysql peer connection, etc... So we are talking about hard disk, mysql concurrent clients, memory, CPU, etc.. Honestly, a server that support that number of users must be larger than the one that you are expecting.
If we talk about 1000 visitors, then the servers specs are reduced but you still need the mysql concurrent peers.
My advice is that you should try and see, most likely the script cost will be the cheapest cost of all your site if we don't consider the domain name.
