Some people will reply that domain names are not case-sensitive. In the new Unicode world this is no longer true.
(Source)
I thought one of the steps in the Unicode > Punycode conversion was a "normalisation", which rendered domain names lower case.
For old-fashioned ASCII-based domain names, Yes, domain names have been and continue to be case-insensitive.
To quote RFC 1035, DOMAIN NAMES - IMPLEMENTATION AND SPECIFICATION:
Note that while upper and lower case letters are allowed in domain names, no significance is attached to the case. That is, two names with the same spelling but different case are to be treated as if identical.
For example, all of these represent the same domain:
In modern DNS, we now have Internationalized Domain Names (IDN) which allows Unicode characters. The problem is that defining upper- and lowercase can be tricky in some languages and character sets beyond ASCII (Unicode is a superset of US-ASCII).
The intent of domain names is to be case-insensitive, but there may be complications with particular characters in particular scripts of particular human languages. So there is no simple YES or NO answer to your question.
If using non-ASCII domain names, you should read: