Can grignard reagents react with any electrophillic sites?
To give you an idea of the nucleophilicity of the two carbons, you may have a look at $\ce{^{13}C}$ NMR data (here for example). These data tell you which carbons have less electron density (the ones which are more deshielded). 

On methyl formate, you'd find $\delta_\text{COO} = 161.8$ ppm whereas $\delta_\text{OCH3} = 50.0$ ppm. This should give you a little intuition of how much the electron density is reduced on each carbon, due to the effect of the electronegative atoms. Clearly, the ester-bearing carbon is much more affected, and this accounts for the general behaviour that you encounter.

However, as Ben Norris pointed out, this is maybe a simplistic picture. In fact, it's not impossible to break preferentially the $\ce{COO - C}$ bond. This is called hydrolysis by alkyl-oxygen cleavage (see here). 

To get back to the question of Grignard reagent, the problem is also explained by HSAB theory. To attack the carbon which is not bearing the ester, you would generally need a "soft" organometallic compound. I can give you an example that corresponds to what you are asking (reference here: Kawashima et al., Tetrahedron 1989, 45, 403.), but note that this is a special case. What drives the reaction is the opening of a strained ring, and the Grignard is modified by addition of copper halide:



I represented this one in particular to show the regioselectivity (breaking of bond represented in red), but the article shows plenty of examples.