I can't tell you from personal experience but I can report what my grammar book and other sources say.
"A concise Polish Grammar" by Ronald F. Feldstein lists the words you mentioned and the following: chłop/chłopu, chłopiec/chłopcu, pan/panu, lew/lwu, kot/kotu, ksiądz/ksiądzu, świat/światu. So yes, kot too belongs to this group of Celownik=-u words.
This agrees with the massive table to be found here
free.of.pl/g/grzegorj/gram/en/deklin_stat.html . They also mention there człek, but the PWN-Oxford dictionary says both forms -u and -owi are possible for this word.
"A concise Polish Grammar" by Ronald F. Feldstein lists the words you mentioned and the following: chłop/chłopu, chłopiec/chłopcu, pan/panu, lew/lwu, kot/kotu, ksiądz/ksiądzu, świat/światu. So yes, kot too belongs to this group of Celownik=-u words.
This agrees with the massive table to be found here
free.of.pl/g/grzegorj/gram/en/deklin_stat.html . They also mention there człek, but the PWN-Oxford dictionary says both forms -u and -owi are possible for this word.