Glad you asked this cause I already booked MK on a now party day. Idk if we will do the party or not. I wasn't sure if I should try and change the day. I'd like to, but idk if it's worth the expense or if my 4 year old would even last. Gives me a lot to think about now!!
Some thoughts: if you have hoppers, starting the day at MK on a party day and then hopping at 4pm is a GREAT idea. You get low MK crowds until 4, then go somewhere else to end your day. Similarly, when you want to see Enchantment, spend your day at a different park, then hop to MK with the plan of camping out for a fireworks spot perhaps with quick service dinner. If you don't have hoppers, you have to decide if Enchantment is a must-do for you. You can arguably get more done on a party day at MK with short hours but low crowds compared to a busy, full hours non-party day during party season. But, if you want the fireworks show, you've got to deal with the crowded day like everyone else.
As to your four year old, how late do they stay up normally? How long into the trip would the party day be? How many late nights / early mornings are you trying to fit in before and after party day?
We took our girls to MNSSHP when they were 5.5 years old, having never been up past 9:30pm prior. (And, that 9:30 was for Disney fireworks. Normal bedtime was 8pm with very, very few exceptions). They made it all the way through to the midnight stage show and they were so stinking proud of themselves. However, in order to make that happen, we 1) did the party as part of a short trip with two park days, one water park day, one party day 2) did not keep them up late at all the nights before the party 3) stayed at the hotel pool the whole day of the party so they had fresh legs and 4) let them sleep in late the day after the party before we headed to the water park. As part of a larger trip, you have to think about how tired your kid will be before the party even starts and how much the party exhaustion will then bleed into the rest of your trip.
We had an incredible time and I would never dissuade someone from doing a party with young kids if they've prepared properly. That said, our friends who were also there had a largely miserable time with whiney kids who were essentially ready to be done before the party ever started. They were on a much longer trip than us and their kids were just too tired to be into it at that point.