If I have osteomyelitis would I be in pain?

Can have pain. If pus in bone is under great pressure bone pain is likely to occur. if cortex or perisoteium of bone contains abscess formation pain is also an issue due to pressure. Sometimes purulent material can cause infarction of bone , another sometimes painful process.
Not necessarily. Most patients i see don't have pain at all, this is because they suffer from diabetes and have neuropathy (lack of sensation). In fact, if they did have the ability to feel, they likely would never of developed the bone infection in the first place.
Not necessarily. While pain can accompany osteomyelitis it is not universally present and the diagnosis is usually made by a combination of history taking, physical examination, x-rays, and lab tests.
DEPENDS. Diabetics, for instance, w/ neuropathy, may not have pain.