Is Bond Formation "Strictly" Exothermic?
Bond formation is alway strictly exothermic in the sense of the change of enthalpy.


  exothermic reaction A reaction for which the overall standard enthalpy change $\Delta H^\circ$ is negative.


A bond can only exist, if it needs energy to break it, i.e. the bond dissociation energy is always positive.


  bond-dissociation energy, $D$ The enthalpy (per mole) required to break a given bond of some specific molecular entity by homolysis, e.g. for $\ce{CH4 -&gt; .CH3 + H.}$, symbolized as $D(\ce{CH3−H})$ (cf. heterolytic bond dissociation energy).


This has absolutely nothing to do with a reaction being exothermic/endothermic or exergonic/endergonic, because this is defined by the rearrangements of bonds.



Regarding noble gas diatomics, it is quite clear from MO-Theory, that there is no bond. However, even these non bonded elements have a non-zero dissociation energy. Please refer to "Why are noble gases stable" and to answers and comments within.