Going from an even number up to an odd number may be difficult to impossible as you need a larger table than was reserved.
But herein lies the fallacy. At WDW, you do not reserve a "table". The policy is that you will be seated at the next available table for your party size. Let's say that you were a party of two and grew to a three. There might be a two top ready when you arrive, and you would have gotten that table. But when you show up as a three, they don't tell you: "Sorry, Mrs. Jones. We had you booked for table #17 which is a two-top and we can't put three people there". Instead, they say: "You will have to wait until the next table for 3 opens up." In the vast majority of cases, they will let you do that. As you can see from the responses on this thread (and all the other preceding threads on this topic), there are two types of responses. Those who have actually tried and have had universal success, (posts 3,5,6,8,10, 13 and 15 below) and those that have not tried but reflexively predict doom, (posts 2,4,7 and 11). So ignore the "I don't think it can be done" responses, and heed the "we did it with no problem" responses.
This doesn't mean that you can grow your party to a size that does not fit on most tables. In other words, If you were a 4 and try to grow to a 7, you may be out of luck.
As for the fire code issues....another red herring. Restaurants set up their tables so that they hold no more than the number of people permitted by code. That means that the configuration is within code if every single seat is occupied. But that NEVER happens (except at banquets, weddings, receptions and the like). Even if all the tables are "occupied", that does not mean that they are at "capacity". There will ALWAYS be parties of 3 seated at tables that hold 4, and parties of 5 at tables that hold 6, and parties of 1 at tables that hold 2. Each of these vacancies keeps the restaurant within code. Also, fire codes account for a fair number of patrons in lounge areas. With the exception of the California Grill, few Disney restaurants have bars or lounges of any significance. So, again, there is a fair bit of leeway such that your nephew is not going to tip the scales. Think about it. If a restaurant were truly at capacity, and I mean real capacity, how could the restaurant keep track of that? They would need someone with a counting clicker counting every time someone walked in or walked out. Parties would not be permitted to enter the restaurant to check in 15 minutes before their ADR because doing so would violate the code. Instead, restaurants eyeball the situation. In reality, if you look at the fire code certificate that shows the permitted number of people, you will be surprised to learn just how many people they are allowed to squeeze in. Sort of like elevators. Next time you are in one that says "Load no more than 12 people", ask yourself just how they could possibly get 12 people into that elevator. The California Grill at Fireworks time is a perfect example. The restaurant is full of diners, the bar is packed, the lounge is full, and yet they still allow more people (who had dined there previously that night) to come up and watch the show. Maybe not everyone gets in, but enough to matter. And yet, there is no violation. Can you think of any other restaurant at WDW that is as overcrowded as the CG during fireworks? Would a rational person really think that growing a party of two into a party of three is going to set off bells and whistles?