It depends on your climate. The Tatarian honeysuckle is not invasive in Russia or China either, but it is here. Euonymus species are often invasive in the eastern U.S., but not west of the Mississippi River. Why would it be any different for honeyberries? Actually, I think Lonicera caerulea is native in Alberta (certainly in Canada), so it's doubtful that improved cultivars would be invasive there. On the other hand, since genes from Japan/China/Korea/Russia stock have been bred in all the selected cultivars, it never hurts to keep a watchful eye.