Does the Michaelis-Menten equation take in account the non-enzyme formation of products?
In any study of enzyme kinetics it is essential to subtract all 'blank' rates and to ensure that the measured rate is due only to enzyme catalysis.  

That is, in kinetic 'parlance', the velocity vs [enzyme concentration] should be linear and go through the origin.  Doubling the enzyme concentration should double the (enzymic) rate, and halving the enzyme concentration should halve the (enzymic) rate. 

Failure to subtract blank rates may give rise to a variety of spurious kinetic effects such as downwardly-curving double-reciprocal plots (Lineweaver-Burk plots).  

Downwardly-curving Lineweaver-Burk plots are diagnostic of negative co-operativity, but such a conclusion may be artefactual if blank rates are not subtracted. 

A very good reference to this sort of this is Enzymes, (1979) by Dixon, M, Webb, E.C.,  Thorne, C.  &amp; Tipton, K.F. (3rd Edn), Longmans,  in particular pp 461 - 462.