Of course it is easier if you start with good gaits. Gaits can be improved, absolutely yes, but if you start with an 8 mover, you have no improvement and you have an 8 mover. If you start with a 6 mover, you will have to ride that much better to get the horse to 7. That is a huge over-simplification, obviously, but if you start with the gaits, everything will be easier. In the past 20 years, there has been much more emphasis put on quality of the gaits - every single test movement talks about quality of the gaits (if you looked at a dressage test from 20 or 30 years ago, you wouldn’t see that language), that more and more people just want to start with the “easy” points if they can afford it - buy the fancier gaits.
But good basics and FITNESS help improve gaits. You can, through riding and training, affect a horse’s balance - if they are using themselves better, lifting their front end more, the reach and scope of the gait will improve. Someone said that a horse must learn to extend and collect - and that isn’t entirely true. The super scopey young horses often offer this up very early in their riding. A less scopey mover is going to develop it through training and fitness.
The other thing to be aware of - the way a horse naturally moves is always going to be something you deal with in training. I’ll give you an example - I have a young mare who is naturally pretty cadenced and rhythmic. She doesn’t have a natural front leg extension though - it has taken her a long time to figure out how to reach OUT instead of lifting her knees higher and higher. She’s getting it now, and it is super powerful looking. However, she was never one to get quick and scrambling, that is not her natural way of moving. When you deal with a horse who just gets quicker, tighter, and shorter when pushed, it is going to be harder to teach them to extend because their natural way is - quicker, tighter, and shorter. Some of the Iberian horses struggle with that, as an example.
So the answer to your question is - yes and no.
