Do Grignard reagents react with amides? Clearly the amide will be unreactive given the poor quality of the leaving group and poor electrophilcity due to delocalization. However, does it react with organolithiums for example?
Amides will react with three equivalents n-butyllithium to give nitriles via geminal lithium oxyimide intermediates (J. Org. Chem., 1967, 32 (11)). n-butyllithium is a strong enough base to deprotonate the molecule twice at nitrogen and once alpha to the carbonyl group. Grignard reagents may well behave similarly.

I do not think this is a particularly useful transformation though because n-butyllithium is a rather indiscriminate reagent. There are a wide range of other methods available - see this paper if you're interested.

In the special case of a N,O-dimethylhydroxyamide, you can make ketones using either.