I believe that the apparent relations are a coincidence.
* The English _swallow (deglutition)_ and _swallow (bird)_ are unrelated, according to the Proto-Germanic reconstructions given in Wiktionary:
* _deglutition_ ***swelganą**
* _bird_ ***swalwǭ**
* _Zhengzhang's_ Old Chinese phonetic series for( ***qeːns** ) suggests several semantic groups which are homonyms:
* Those relating to _food_ (, - _banquet_ )
* Those relating to the bird (, , possibly - _horse with a white backside_ )
* Those relating to a proper noun (, )
* A word meaning _beautiful_ ()
Coincidental homonyms for unrelated words are possible for any language, and it is likely that the Chinese words are just that.