As goofieslonglostsis mentioned, if the plane has a center entrance, you may be able to get the wheelchair onto the plane and close enough to transfer to the airplane seat without using an aisle chair.
If you do need an aisle chair, airline staff will help you to transfer to it, wheel it on board and help you get into the seat.
If you are going to use an aisle chair, it's much easier to do that when preboarding, so they will usually have you preboard.
Here are some pictures of DD with an aisle chair.
There is also further information in post #15 of the disABILITIES FAQs thread near the top of this board (or you can follow the link in my singature to get there).
I can't speak for Southwest because we have never traveled with them, but I can speak of experiences with air travel with multiple airlines over the past 20 years.
In the 'way past' everyone with wheelchairs were pre-boarded automatically, whether they wanted to be or not. You did not have to ask or tell the airline that you wanted to preboard, the gate agents were aware of who in the gate had a wheelchair and just came and got you.
I know that some people with wheelchairs did not want to preboard, but the policies (official or unofficial) of most airlines 20 years ago was that they had to.
After the Air Carriers Access Act (the air travel parallel to the ADA) came into existance, passengers could no longer be required to preboard. Our personal experience is that once it came in, we have to ask to preboard. Sometimes, they will announce preboarding, sometimes not unless you ask.
There are some advantages to preboarding -
One is that you have more time and space to board without other passengers being close around you.
Another is that if you have assistive and/or mobility devices (or in our case, pieces of DD's wheelchair), those have priority for onboard storage,
if you choose to preboard. If you do not choose to preboard, if those areas are full when you board, you are out of luck.
Preboarding also gives more time for the baggage handlers to get your wheelchair/
ECV down to the baggage compartment.
We have always preboarded with our whole party. Usually it's only DD in wheelchair, DH and me, but we have preboarded with as many as 5, not children. Because DD's wheelchair needs to be partially taken apart, we would not be able to preboard with just one person besides her - we also have each of our carryon bags.