Is there a connection?

Probably not, or Anu would've mentioned it. The street in London, Pall Mall, is named after the game pall-mall (via French palle maille) from Italian pallamaglio, literally 'ball mallet'. We get our word mall as in shopping mall from this, too.

Pell-mell is from French pêle-mêle < Old French pesle mesle probably a reduplication of mesle the imperative of mesler 'to mix'.

English (as well as other languages) has many examples of these rhyming pairs of words: cf. helter-skelter, Hoppelpoppel German 'scrambled egg dish'.

Ceci n'est pas un seing.