Can A Rose Choke A Rose of Sharon??

Old Rambler in the Rose of Sharon

It has always lurked at the picket fence that divides my yard from the neighbor’s, and I though I thought it was pretty, I really didn’t pay it much heed.  So, imagine my surprise yesterday morning when I saw deep crimson blooms in the rose of sharon.  First the tree gets pink flowers.  Second, it doesn’t bloom this early in the season.

The deep crimson is the old climbing rose that has grown tall and sturdy through the branches of the rose of sharon.  What a pleasant and unexpected surprise.

Does anyone know whether a rambling rose can choke a rose of sharon?  Should I cut those canes that are so wonderfully laden with blooms?  Or should I nurture its rambling nature?