Yes of course, the more profit that minner bitcoin get the more people want to be bitcoin minner the more people who interested to bitcoin then the price of bitcoin will be increase, its about sentiment, if people think that there are many good potential in bitcoin then people will buy bitcoin thwn cause to the increasing price of it.
I also think that way but as we can see number of miners did not affect the price of bitcoin. Usually, if there are lot of miners then probably it is difficult for a block to mine. The mining is difficult and it is unprofitable if there are lot of competitors in mining.
It would affect the price of the coins on the market if the miner decided to sell all the coins that he made from mining Bitcoin.