No, it's not necessary to buy your tickets in advance; it just saves you having to stand in line for tickets and the lines, at certain times, can be long. I would suspect that there would not be much of a line at 3pm to buy tickets, mainly because most people will have already entered Mt. Vernon by then. Mt. Vernon closes at 5pm and two hours barely gives you enough time to really see much of it.
If that is the only time that you can go, then I would advise you to get in line for a tour of the mansion right away. (The weather is supposed to be very nice this weekend, so there could be be big crowds and a long line for the mansion tour, even after 3pm.) I don't know if Mt. Vernon is still offering timed tickets as was discussed in this thread.