Of the inn keeper? Absolutely not! I mean, this is Rangiku we are talking about here! The woman has all of Seireitei throwing themselves at her feet! Why on earth would she be jealous of a inn-keeper who wasn't even that pretty? Believe me when I say Rangiku is fully aware she has Hisagi wrapped around her little fingers and it'll take more then Hisagi showing his customary gentlemanly behaviour to a rather plain inn-keeper to get her jealous.