Yes travelling with a hollow back can cause a sway back after years of working like that, some horses will get one others wont.
With a hollow, or stiff backed horse, there is absolutely no way that you can get collection, so don't even think about that at the moment.
A horse that moves with a stiff/hollow back is going to be difficult to sit on, will never come soft and off the forehand, and as I said above, will never get collection.
A horse hollows its back for any of a number of reasons, most often it is simply rider error/inexperience, but it can also be because of ill fitting tack, soreness, discomfort or just because the horse is built that way - for example many arabs are difficult to get 'over the back' because they are built quite hollowed out.
Hopefully this girl will start working your horse long and low. This is the best work to get a horse to round its back and use it, rather than hollowing and stiffening. Ideally your horse should be shaped like a rainbow when in long and low - head and bum down, back nice and rounded ;)
There is very little point in asking a horse whom has travelled hollow for a long time, to come straight into a 'competition' frame. It takes a lot of strengthening and relaxation work to build the back up enough for the horse to be able to lift and swing through the back. To get a horse to 'swing' takes a skilled and knowledgable rider, and often many just don't have the feel to know when the back is genuinely working, so I hope your friend is someone who has a decent feel and knows how to ride the back swinging - it would be of great benefit to your horse.
I would ask her NOT to work on 'collection' as yet, your horse is not being stubborn, it is physically impossible for her to engage her hind quarters and lift the forehand, if she is stiff and hollow in the back. A very good reason for her to jack up.