Grignards and diatomic halogens
Can Grignards react with diatomic halogens as to perform an
  substitution reaction?


Yes, but it looks like a mixture of products results, including something explosive.  Here is a link to an abstract of some early work that reports,

"Chlorination of Grignard and Iotsich reagents, RMgX, (where X = Br, I) gives considerable quantities of RI and RBr together with RCl. Bromination of RMgI results in RI and RBr. Bromination of RMgCl leads to RBr, and iodination of RMgX (X =Cl, Br), to RI." 

An "Iotsich" reagent is an acetylenic Grignard ($\ce{RC#CMgBr}$)

Judging by the fact that 1) the abstract suggests that product mixtures of the various possible alkyl\aryl halides are often formed and 2) no further reports claiming synthetic utlity have emerged, I suspect that the reaction is of limited synthetic value.  Nonetheless, your initial suspicion that reaction should occur seems supported.

One further note, many MSDS's and "Hazardous Laboratory Chemicals Disposal Guide, Third Edition" report that when phenylmagnesium bromide is reacted with chlorine, a solid is formed that explodes when shaken.  The reference provided is the same J. Organomet. Chem. paper cited above.  Given the lack of detail provided on the solid, my guess is that it wasn't characterized.