Normally you being there in plenty of time should ensure you are the first-came, and excess passengers would be put on after the rest of you. However, this is Greyhound we're talking about, and to further complicate, this is Thanksgiving, the day of the year rules just don't apply ;)
According to one source:
As the ticket policy suggests,
Greyhound does not assign you a seat when you buy a ticket. If you
show up at 8 AM for your 8 AM bus, the bus may be full. If you show up
at 7:30 AM and the bus line already has 55 people in it, you may not
get to ride that bus. If you're riding for your first time, you will
get a good seat on your bus if you arrive an hour ahead of time, and
will probably catch it (unless you need to check bags) if you arrive
fifteen minutes ahead of time.
For the expert, how early you show up can be calculated by four
variables: (1) Are you checking bags? (2) Is your bus "originating?"
(3) Is your departure station popular? (4) Is the route popular?
If you're checking bags, you will have to wait in line. Depending on
station , you may have to wait in the
general ticketing line. At peak times, there can be 30 people in the
general ticketing line--all of which have urgent needs. You don't have
a choice about waiting, so budget 15-30 minutes.
An "originating" bus means that your bus will be empty when boarding
begins. If your bus is originating, you can show up later, because
more seats will be available.
If your departure station is popular (i.e. a large city), more people
will be in line, so budget another 15 minutes. If the route is popular
(and most are, especially on the weekends and at night), you may wish
to budget another 15-30 minutes.
Your best situation is an originating bus, leaving from small town X,
at 10 AM. Your worst situation is a North Hollywood bus originating in
Los Angeles, CA going to San Francisco at 10 PM on a Friday night.
So given all that, I'd try and get there as early as you possibly can. Because after all, this is Thanksgiving, and you'll already be thankful you have a seat ;)