I think that the formation of the Grignard will be inhibited. The formation of a Grignard is an autocatayltic reaction. It is well known that one of the best ways to get a Grignard synthesis going is to add some of an existing solution of a Grignard reagent.
I reason that as soon as any of the Grignard forms then it will be consumed by the reaction with the ketone. As a result the reaction of the alkyl (or aryl) halide with the magnesium will be so slow that for all intents and purposes we can say "nothing happens"
It will be like trying to make a Grignard in ether that has a trace of water, I once tried to make methyl magnesium iodide and failed. I then discovered that the ether was not as anhydrous as I thought it was. I am sure that if something is present that destroys the Grignard as soon as it forms then the rate of the reaction of the magnesium with the alkyl or aryl halide is so slow that as a synthetic reaction we can regard the reaction as being "useless".
When I tried to make the Grignard in the slightly damp ether, I tried adding iodine, I tried ultrasound and even these things were not able to get the synthesis of the Grignard going. I have always found that if I exclude water strictly from the reaction (bake all the glass equipment overnight before use and sodium dried ether) that the synthesis of a Grignard never fails. What I do is to stirr the magnesium under nitrogen for a long time. I then add a little ether and some of the alkyl halide and I leave it with no stirring for a while. This normally gets it started.