The transformer should not need a gap, so long as the max volt-time product applied to the primary is clamped to an appropriate limit, and the duty cycle is kept under %50. For the inductor that depends completely on the design details, but in general chokes with ferrite cores will require some gap.
Clamping the volt time product is done by the controller, not by the converter circuit itself. The controller has a duty cycle clamp built in, and will always be clamped to <50%. But a volt time clamp means that the clamp level is variable, and is inversely proportional to the input supply voltage (but it's never allowed to go to more than %50, unless you have some kind of fancy active clamp circuit). Many control ICs have this stuff built in.