This would simply dilute the rate at which transactions are confirmed. In fact, the only thing it would do is make the first confirmation of a transaction take (statistically) twice as long.
If someone came in with 50% of the network and started computing blocks with no transactions, then before the next retarget (difficulty change), one block would be generated every 5 minutes, with half of them containing transactions. After the difficulty change it goes up to 10 minutes. Now if you send a tx at this point, it will be (on average) 10 minutes until the next block is produced. Half the time this won't contain your transaction, half the time it will. So you could wait 1-4 blocks for your confirmation instead of one (with the higher numbers being more unlikely).
However, after that first confirmation, all blocks produced after it will count as confirmations, so you'll continue to to accumulate transactions normally after that.
On the other hand, "difficulty" is not just difficulty of producing blocks, but also difficulty of someone attacking the network. So if this person who has 50% of the network decided to use their power to do this, instead of executing a "real" attack on the network, we should be lucky. They're making the next person who wants to attack the network double their computing power requirements.
Although, as memvola said, the way the blockchain is structured, there's no good reason not to include tx's in the block the miner is working on. If you have ill-intentions towards the network, there's a lot nastier stuff you could do with 50% of the computing power. If you don't have ill-intentions, you would just include the tx's and collect your fees.
Really well said!