bottle brush companion planting

I have a bottle brush in my front garden among some other lower growing plants like Mock Orange and a few hardy natives. The bottle brush is a bit sparse and open in the lower branches and I want to thicken it out as this planted area provides a screening effect from the street. What I am considering is whether an older variety climbing rose might be compatible in that garden environment? I want to make sure that if I did this that it won’t put Tui’s off from coming to the bottle brush flowers in the late spring?