Thank you for asking your question on Just Answer. From the information you have given me, the growth is not considered a rose sucker. Suckers on roses are produced by the roots and where the graft is attached to the root stock. If the sprout is coming out below the graft, then it is a sucker. I will include more information shortly. My computer requires a reboot at this time.
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It is important to remove a true sucker since it will take the strength away from the rose graft. The image below may help with the identification of a rose sucker.
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