Hospitals are complicated, but I don't believe they usually make injuries any worse - at worst, they provide a centralized place for your dwarves to die.
They can facilitate recovery from anything, but you pretty much HAVE to have it fully supplied with the following:
- Chief Medical Dwarf, with the Diagnosing skill enabled. For large forts, I suggest disabling all other labours for this dwarf.
- Dwarves with all other healthcare labour options enabled - wound cleaning, suturing, surgery, bone setting. Once more, it's a good idea to have dedicated dwarves for this.
- The hospital needs to have beds, chests/boxes/bags, table(s), traction bench and a source of clean water
- For supplies, you need to have thread, cloth, buckets, splints, crutches, soap and gypsum plaster
Clean water is IMPORTANT - if you are using a well, it has to draw water from a source 2z deep, or a moving water source. If the source is 1z deep still water, it will be stagnant and/or laced with contaminants. In that case, cleaning the dwarves' wounds with this can make it worse.
To check, use (t) to view the components of a well, and examine the bucket. It should contain the water. If it's stagnant or laced with mud (or worse), you need to rebuild the well.
I have had dwarves survive the loss of two limbs and breakage of everything else. (a really unfortunate incident with a giant eagle) That particular dwarf became a farmer
EDIT: One thing to be aware of is that hospitals can also be a spread vector for contaminant fluids, such as the stuff produced by certain underground beasts that I forget. Those dwarves, regretfully, should not usually be allowed back into your fortress - unless you have a decontaminating chamber available.