If you define the mid price as the average of the best bid and best ask price the answer is no. If there are bids for 10 lots @ 10.00 and asks for 10 lots @ 10.10 markets orders smaller than 10 lots will not affect the mid price. The mid is 10.05 before and after.
This also implies that no trade is necessary to change the price. If the best bid or ask changes, the result of $$\frac{\mathrm{best\,bid} + \mathrm{best\,ask}}{2}$$ will also change.