It is generally possible as there are a huge number of accommodations available. Unless you arrive during a really popular holiday, I would expect you to find some availability. Of course, it is impossible to say this with certainty. It will diminish your choices for sure though which will depend what you are looking for. The most desirable locations do get full though, particularly in less touristy cities that have a limited number of nice hotels.
The things to balance here are predictability, flexibility and cost. Reserving in advance guarantees your price in advance but if you book locally, you can often get a much cheaper rate than the same property online. I saw the average difference was around 50% by comparing with other travelers. One has to be really careful in Vietnam though because if you simply ask, there are people that charge double or triple on the account that you are not expected to know the real price. This is particularly true of transportation like Taxi and Motos.
If what you are looking for is to keep your itinerary flexible, then my recommendation is to book the few days of hotel at your arrival city ahead of time and then in Vietnam, while travelling, you book the next destinations as your schedule firms up. Booking via trusted locals can get you very good prices. This is often my strategy when there is time for flexibility. On the other hand, if your schedule is tight, book everything ahead and you won't waste time on location figuring how what is where and the fare price!
Keep in mind that taxis are very expensive in Vietnam and so if you need more of them because you saved a few dollars on a further hotel, then you will end up paying more.