Transactions are incorporated into blocks, right?
Yes.
Each transaction's hash is incorporated into a hash tree, whose root is stored in the block header. Every new transaction changes that merkle root.
That means every transaction that is incorporated into a block will change the block's hash. So let's say a server has just an average speed processor which might take a week or more to generate a block. Does it stop incorporating transactions when it's begun a search for a conforming hash, or does it just keep throwing them in there and changing the nonce as well? Seems like it has to be the latter.
Remember that you don't "lose" any progress, or work, by hashing a different block header, with an updated merkle root.
The probability of finding a hash is the same either way.
