There are a couple terms being synthesized loosely. While it is true that in the classical sense, inflation is an increase in the money supply, the end result does not always equate to increased prices. Price is a function of both supply and demand, therefore the slogan "to many dollars chasing too few goods" only implies if the demand for dollars decreases relative to the demand for that specific good.

Could more dollars in the system cause this to happen? Sure, but i highly doubt the lowest income earners increase in volume would be enough. Reason be, a firm's revenue might increase as the result of more disposable income from a demographic that has a steady % of their budget allowing the purchase of the specific firms good or service.

With this in mind, the real question is whether an increase in minimum wage reduces the instances of employment (jobs shifting overseas) as opposed to an increase in m2. If the decreased cost of production equals lower prices, equal to the lost revenues (short run) due to lost employment, than it is a positive outcome (long run).