Great question, Sylvia (in Duluth).
The short answer: Yes, as in many songbirds, including most wood-warbler species in the USA disperse (BUT do not necessarily migrate) soon after their nest is independent of their newly-born hatch year clutch.
Now the answer gets more complex: 1) Dispersal occurs for all wood-warblers away from the nest, but some species likely go farther astray from the nest than others. 2) Then, if the wood-warbler species is an obligate migrator from the northern latitudes (e.g., upper Midwest or New England as two valid examples), it will eventually migrate from its dispersal grounds.
Note I’ve introduced the concept of “dispersal” and “migration” above. They mean different behaviors, with dispersal a pre-migration behavior that includes foraging to “bulk up” and add calories for wood-warbler species that need to have plenty of fat for their upcoming post-breeding migration to over-wintering grounds.
Migration is the short or long distance trek birds (including most N. American wood-warbler species) undertake as early as July (e.g., Tennessee Warbler and Yellow Warbler are known to be early nest site dispersers and, hence, migrators south). Laggards that may leave later than other south-bound wood-warbler species include Yellow-rumped, Palm, and Common Yellowthroat, though, of course, Christmas Bird Count results in wintery, inclement areas have detected several other wood-warbler species beyond the aforementioned three.
Meanwhile, if you’ve read this far, congratulations. Wish to know more about this topic? I suggest you consider reviewing the following links: 1) https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=Parulidae+Wood-warbler+migration&oq=wood-warbler+migration and 2) https://royalsocietypublishing.org/doi/abs/10.1098/rspb.2011.1045
Regards and best birding, Daniel Edelstein, DanielEdelstein@att.net, 415-246-5404 (WarblerWatch.com features my Bird Guiding and bird tour information, as well as my resume, etc., et al.)