Can I avoid being limited by IIS's ten-connection ceiling if I transfer files through sockets? I'm using Windows XP.
Technically the answer is yes, but, you will not be using IIS if that is the case.
As I said at your previous question, you can use Apache Web Server or Filezilla FTP Server if you want to transfer files.
No, you can't avoid the concurrent connection limit (unless you're willing to patch TCPIP.SYS, which is not officially supported by Microsoft) because Windows XP is limited to 10 simultaneous inbound connections by design:
Run IIS 5.0 and IIS 5.1 Instead of PWS on Windows 2000 Professional
There are ways around this that work, but these are not officially supported by Microsoft as they involve modifying Microsoft's TCPIP.SYS file (where this concurrent connection limit is imposed), and if TCPIP.SYS gets updated in the future you'll have to figure out how to patch the new TCPIP.SYS file (or wait until one of those third party patching programmers figures it out).
The better solution is to use an OS that is more capable by design. I've heard that Windows Server 2003 might not have this limitation (but I've not confirmed this), and I know for a fact that Unix and Linux are definitely capable (I use NetBSD to support web sites that regularly get hundreds of concurrent connections without any trouble).
A few notes about alternative solutions
If you know that your web site will be very busy, I highly recommend you consider a proven technology like Apache HTTPd (as @William Hilsum smartly suggested, which is available for Windows, Unix, Linux, and most other Operating Systems).
For FTP, on the Windows OS the FileZilla solution is excellent (as @William Hilsum also suggested), and in the Unix/Linux environments there are many other options that might fit better (I particularly like ProFTPd because its configuration file format is just like Apache HTTPd's excellent configuration file format).