Of course he could have won; I mean, he won the popular vote after all. He lost by a maximum of 0.2% of all total votes cast in the states of Alaska, Missouri, New Jersey, Ohio, and Illinois combined.
If Humphrey hadn't won every single one of those states (with the exception of Alaska), it would have been thrown to the House, where Nixon had a good chance of making a deal with the Southern Democrats and Wallace.
If Nixon had won every one of those states, he would've been president.