score:16
Yes, your suspicion is correct. Once man had boats (no later than 40,000 years ago) and the ability to live in the arctic, the island chains strung across the Bering Strait could not have been a significant barrier. There are native peoples who traverse it regularly today using native methods.
As for evidence, archeologically we know about the Thule people (ancestors of today's Inuit), whose culture is first found in the Chukchi Peninsula (Asian side of the strait) and the Bering islands around 200BC, and spread eastward across the strait and clear to the Atlantic Coast of North America.
Linguistically there appear to be no less than 3 waves of immigration that occurred across the strait (4 if you count the Inuit). Genetic studies show at least 2 (3 if you count Inuit), with the Na'Dene people almost certainly having come over after the land bridge submerged 15,000 years ago. Thus boats would have been required.
Genetic flow over Beringia
Present-day distribution of Na'Dene
For these reasons, very few scholars still argue that the only immigration from Asia to the Americas happened over an Ice Age land bridge.
Upvote:5
I recently read a book, Across Atlantic Ice: The Origin of America's Clovis Culture that purports to challenge the foot traffic in two ways - first that ancient peoples were far more handy on boats than current thought, so a foot path isn't needed for them to spread, and second that evidence for passage from the Bering area is fairly thin in the period where land bridge was in place. They then try to show that the Clovis point culture has links to Europe and evidence seems to show that it spread from East to West.
While this isn't a direct answer, the authors try and show that the use of boats and pack ice, like the Inuits do today, can allow spread over oceans without the need of a land bridge, forming a pack ice bridge that can be lived on during transit, and they do discuss evidence for migration into and from Alaska (to refute or mimimize it as an answer to the Clovis peoples) that might directly answer the question.
I found the book interesting.