The mini plan can not at least no more than a few miles
offshore.
With Roam once you get a few miles (it varies from 2 to 10)
offshore it will stop working unless you enable priority data on a pay as you go basis ($2/GB). With priority data turned on you can use it across an entire ocean and turn priority data back off
At least right now there is no option to enable Priority data on a pay as you basis for the mini plan so like Roam once you get a few miles offshore it will stop working except there is no option to restore
service. When you get back closer to land it will start working again. That makes it useful for inshore, and coastal cruising but it wouldn't be useful for crossing oceans. The mini plan right now is also country limited. Per the terms the mini plan purchased in the US can only be used in the US although there are reports that SpaceX is not enforcing that yet.
To be clear you can use the mini dish but must have the regional roam plan not mini roam plan if you want full offshore
service.