All of my cleanings have been done with the wire removed except one. The ladies cleaning my teeth always thank me for removing the wire, it is a lot easier for them.
Whether or not it makes a difference cleaning wise...not so sure. Although, the one time I didn't have the wire removed, it didn't feel as clean to me for some reason. Maybe you can ask them.
I have self litigating brackets so when the wires come out, the ortho girls will leave my gates open and use the air sprayer to get any food that is stuck out before they close them for the cleaning.
I try to schedule my cleanings for when I know we will be changing wires so it isn't a big deal to get the wire out. My ortho and dentist are a 3 minute drive away so it is convenient for me.
I really don't think it matters either way. The important
thing is, getting your teeth cleaned.