Yes, I do believe that this is what Tolkien implies
We can for example see that the names of the Kings of Rhovanion are Gothic in origin
Quote:
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It is an interesting fact, not referred to I believe in any of my father's writings, that the names of the early kings and princes of the Northmen and the Éothéod are Gothic in form, not Old English (Anglo-Saxon) as in the case of Léod, Eorl, and the later Rohirrim. Vidugavia is Latinized in spelling, representing Gothic Widugauja ("wood-dweller"), a recorded Gothic name, and similarly Vidumavi Gothic Widumawi ("wood-maiden"). Marhwini and Marhari contain the Gothic word marh "horse," corresponding to Old English mearh, plural mearas, the word used in The Lord of the Rings for the horses of Rohan; wini "friend" corresponds to Old English winë, seen in the names of several of the Kings of the Mark. Since, as is explained in Appendix F (II), the language of Rohan was "made to resemble ancient English," the names of the ancestors of the Rohirrim are cast into the forms of the earliest recorded Germanic language. ~ UT, Cirion and Eorl, note 6
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So we do see that as far as languages are concerned, the Rohirrim clearly would represent the Anglo-Saxons. The Beornings and the Woodmen of Mirkwood are said to have also been related to the people of the Eotheod, so they also must represent some people related to the Anglo-Saxons, probably also originating from the Goths.
Picts and Celts had different ancestors. The Beornings are inspired by berserkers from Norse mythology, so its pretty hard to find them a corespondent in real history, perhaps some Norse tribe. The Woodmen would in my opinion rather be Jutes or Frisians.
As far as their