No, indexing shouldn’t affect it. The operation is performed synchronously on the client machine, meaning it happens right away on your computer. Or it should.
The move operation consists of two distinct steps, a copy followed by a delete. The delete may not be successful due to permissions problems, for example. Since you stated that the file is on your desktop, it’s unlikely that you don’t have permissions to delete it, but you should check that anyway.
Sometimes files or folders cannot be deleted or renamed due to ‘another process accessing the file’. If this is the case, close the process accessing the file. Occasionally, you will find that there is no process accessing the file but Windows thinks there is. The only recourse that I have found in this case is a system restart.
Hope this helps,
Faan