Nope, no problems carbonating if there's no headspace, in fact it can make force carbonating easier. Theoretically the reduced surface area for absorption of CO2 with no head space could slow carbonation but in practical terms it's not an issue.
For open filling I fill the keg first with CO2 from the beer dip tube, ie bottom up - the grey line pushed and held onto the beer in will do - 30 secs is ample. then fill to the absolute brim. That way oxidation is utterly minimised. This is my preferred way of filling a keg and will fit 20 or more litres in a keg easily. Oxidation is minimised but you do need to make sure when connecting the gas line that it's on a non return and pressurised circuit - which can either be with fancy non return disconnects or a manifold with built in non return.