No. Each person’s eligibility and actual immigration status require assessment. Residence alone does not establish permission to live, study or work in the United States. Plan each person's dates separately. A dependant's authorized period is derived from the principal's and can be granted shorter than the household expects, while school registration, a lease and a spouse's employment authorization each answer to a different calendar and a different office.
Review each family member’s actual documents
Qualifying L spouses are employment authorized incident to status with appropriate documentation. Children receive no work permission solely through L dependent status. Identify citizenship and intended activities separately for each person when planning the process.
Where a family has lived in more than one country, the practical delay usually comes from documents rather than from decisions. Civil records, marriage certificates and birth registrations issued abroad may need retrieval and translation, and the issuing authority's processing calendar is outside anyone's control. Start those requests when the transfer is first contemplated rather than when the filing is assembled.
A shortened grant to the principal contracts every dependant's period at the same moment, so name in advance who would stay, who would travel and on what date. A spouse who intends to work should know that the authorizing documentation has an issuance timeline of its own and should avoid committing to a start date before it exists.