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The answer to the question in the title is "it depends"; the answer to the question in the body of the question is "yes" see below.
"New states have generally been admitted after a period of territorial government, during which Congress and the President have broad authority pursuant to the Property Clause, also in Article IV, Section 3. An Act of Congress established the territorial government, often giving greater self-government (e.g., in the form of an elected territorial legislature) as the territoryβs population increased over time. Some states, however, such as California and Texas, have been admitted without ever being territories." ConstitutionCenter.org
If a territory is administered by the Federal government, then Federal law applies. If a territory is admitted without having been administered as a territory, then, no.
Spurred by the nationalism aroused by the Spanish-American War, the United States annexed Hawaii in 1898 at the urging of President William McKinley. Hawaii was made a territory in 1900, and Dole became its first governor. state.gov
Hawaii, administered as a federal territory, would have been subject to Federal law