I don't think the Hatch Act would preclude Q posting.
For all we know, Q team might be a private entity receiving intel directly from the president and therefore not subject to the Hatch Act.
Q team could also be military (similarly exempt from the Hatch Act).
The Hatch Act applies to executive branch employees (excluding POTUS, VPOTUS, and the Military). So, that means, DOJ, FBI, etc.