Yes. You can have it swapped from long billet to short, or vice versa. Depending on how your saddle is constructed, you may or may not need a saddler to do it. The billet of my saddle is attached to nylon webbing, which in turn attaches to the tree, so if I want to change billet, all I need to do is to unsew it from the webbing and attach a new one.
As to preference, it's hard to say. It's easier to adjust girth while mounted with short billets (for me at least) but it's less bulk under my thigh with long billets... Though it is harder to find long enough black girth to match your black saddle if you have short billets. Nowadays most dressage girths are made to go with long billets.