The Spatial Evolution of Young Massive Clusters III. Effect of the Gaia Filter on 2D Spatial Distribution Studies

[Context.] Gaia is limited in the optical down to G~21 mag so it is essential to understand the biases introduced by a magnitude limited sample on spatial distribution studies. [Aims.] To ascertain how sample incompleteness in Gaia observations of young clusters affects the local spatial analysis tool INDICATE and subsequently the perceived spatial properties of these clusters. [Methods.] We created a mock Gaia cluster catalogue from a synthetic dataset using the observation generating tool MYOSOTIS. The effect of cluster distance, uniform and variable extinction, binary fraction, population masking by the point spread function wings of high mass members, and contrast sensitivity limits on the trends identified by INDICATE are explored. A comparison of the typical index values derived by INDICATE for members of the synthetic dataset and their corresponding mock Gaia catalogue observations is made to identify any significant changes. [Results.] We typically find only small variations in the pre- and post- observation index values of cluster populations, which can increase as a function of incompleteness percentage and binarity. No significant strengthening, or false signatures, of stellar concentrations are found but real signatures may be diluted. Conclusions drawn about the spatial behaviour of Gaia observed cluster populations which are, and are not, associated with their natal nebulosity are reliable for most clusters but the perceived behaviours of individual members can change so INDICATE should be used as a measure of spatial behaviours between members as a function of their intrinsic properties (mass, age, object type etc.), rather than to draw conclusions about any specific observed member. [Conclusions.] INDICATE is a robust spatial analysis tool to reliably study Gaia observed young cluster populations within 1 kpc, up to a sample incompleteness of 83.3% and binarity of 50%.