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.
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: