Well, randomness has its fans, but a bit of story definitely helps readers understand the characters more and make them appreciate them more.
Basic things help such their backgrounds, their likes and dislikes, their family and friends maybe... It doesn't need to be super story driven, just give the characters some 'fleshing out' as it were.
Like maybe a character is crazy afraid of mice...and you give a bit of explanation for why. Doesn't have to be full on story arc stuff, but maybe they woke up one morning with one staring right at them on their bed.
Just throwing out my thoughts here given my own comic was originally just a 'gag-a-day comedy' but I started early on giving my characters backgrounds and stuff as I felt people might like that.