First, we should say that buckthorn can be an invasive plant. See this article for more information: Buckthorn
If the buckthorn (Rhamnus cathartica
) still has berries on it, the seeds will probably germinate after the branches are chipped and spread as mulch. In fact, the mulch will provide a favorable growing medium for them. Although buckthorn seedlings are easy to pull, they may not all come up at once, so getting rid of them will probably require weeding for a couple of years.
If not a lot of berries are present, you may be able to snip them off before putting the buckthorn into the chipper. You could also eliminate most of the seeds by composting the chips, but the resulting product would not provide a long-lasting mulch.