I don't get the warning message

It's not a warning. It's a fatal error. It was added to newer versions of Perl.

I also noticed some differences in the content of the resulting dbm file

Not here. 5.8.0 with Encode, 5.8.0 without Encode and 5.8.8 with Encode output:

0000: 02 00 FE 03 FB 03 00 00 00 00 00 00 00 00 00 00
0010: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
0020: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
...
03D0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
03E0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
03F0: 00 00 00 00 00 00 00 00 00 00 00 62 61 72 D7 90
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Since strings of chars are stored internally as UTF-8, the resulting file is indentical.