While you would NOT file a State tax return for a single-member LLC in those states, you are required to a file State income tax return for the holding company LLC to report the income from each state.
According to the Alabama Dept of Revenue, a single member LLC should not file a separate Form 65.
Per the Georgia Instructions for Form 700, under Filing Requirements, an LLC is required to file a Georgia return only if also filing Federal Form 1065.
The Maryland Admin Release No. 25 states that if an LLC has elected to be classified as a disregarded entity for federal income tax purposes, [it] will not have to file a separate Maryland income tax return.
According to the Virginia Dept of Taxation, only pass-through entities are required to file a tax return; single-member LLCs are specifically excluded from the list of pass-through entities.
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