Let me start by saying that I have never heard of the parks reaching capacity during Thanksgiving week. While nothing is guaranteed and unanticipated crowd convergences could
happen any time, typically the only days of the year that you might
anticipate full capacity crowds are July 4 and December 24, 25, and 31.
And this doesn't even happen every year.
When crowd control does happen, it occurs in phases. This is described very well by Moms Panelist Bret
here.
In the
rare instance when there is a Stage 4 crowd control in place,
that means that no new guests will be able to enter the park. That
means no guests, not annual passholders, not DVC members, not people
with dining reservations. If Stage 4 is in place, the park is at it's
full legal by-order-of-the-fire-marshall limit. In this situation, you
would be unable to go to your dinner.
My advice to you would be if being in
a certain park or dining at a certain restaurant on a holiday is a
priority for you, plan to be there as far in advance as possible. But again, I have to say I think it is extremely unlikely that you will encounter this situation.