Yes! All bitlinks are case sensitive. This means if your bitlink is “bit.ly/CustomWord”, then “bit.ly/customword” will not work and bring you to an error page, or to another long url destination, as it is registered as a different bitlink.
You can make both work however, if you edit your bitlink to the other casing options. Edit your all caps link to be all lowercase, or any variations you think your recipients might type in.
Editing your bitlink combines metrics for all versions of the bitlink, and they all will direct to the same initial long URL.