I need to sync a folder with around 13,000 files, adding up to about 21GB in total.
Can I sync this folder or is there a limit on files?
The free ubuntu one service is limited to 5GB.
See https://one.ubuntu.com/services/ for prices for more than 5GB.
Regardless of whether it is free or the level you are paying to have for your file sync, my experience has been that there is some issue on file size. Whether this is true or not, it appears from what I have seen that large files are not going up on just one pass at the process. A Ubuntu One IT professional should address this issue with a view towards providing a realistic expectation for users.