If you asked this question in 2010 the answer would most simply be yes. Miners have the special ability to choose which transactions to include in blocks they mine, and also the order of those transactions. Miners don't have a limit on what they can do in this regard except for one thing currently, which is blocks can't be over 1MB in size.
Now in 2017 blocks are basically full at 1MB, so miners are more selective about which transactions they include. That's why the higher the fee you pay the more likely your tx(s) will confirm soon in a block. Pay too low a fee the way things are and your tx may never confirm. This is at the heart of the "block size debate".