The tilde character may have a totally different meaning in Windows, and I would consider it invalid – or at least ambiguous – to use it to refer to the user's home directory.
On file systems that do not support long file paths, the tilde would be used as a replacement character:
A long file name is considered to be any file name that exceeds the short MS-DOS (also called 8.3) style naming convention. When you create a long file name, Windows may also create a short 8.3 form of the name, called the 8.3 alias or short name, and store it on disk also.
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On many file systems, a file name will contain a tilde (~) within each component of the name that is too long to comply with 8.3 naming rules.
You can read more about 8.3 filenames on Wikipedia, which is a legacy file naming convention that dates back to the times of DOS.
That said, modern programs may indeed use ~ as an alias for the user's home – PowerShell for example, see @Broam's answer. And of course there is a difference between having the user type something that the shell then interprets vs. what a shell may output. However, as you cannot assume users to use PowerShell, or be knowledgeable about Unix conventions, I'd recommend against it.