You've asked a question which we can't answer easily. It's a good question and you've put forth some interesting points..
Parkinson's disease is a chronic, incurable, progressive neurodegenerative disorder which has both motor and non-motor symptoms. PD is a collection of syndromes with varying symptoms and varying rates of progression. Therefore, if your father actually has PD, it would be difficult to predict his progression.
To see the generalized progression stages, read the article and look at two of the PD rating scales in the linked article.
http://parkinsonsfocustoday.blogspot.com/2009/03/questions-about-parkinsons-disease-part_3744.html
Chris has provided some excellent information about the possibility of a misdiagnosis. Without a diagnosis by a neurologist specializing in motion disorders or sometimes just a physician who specializes in parkinsonian disorders, you father my not have received the proper diagnosis. Until the lab diagnostic tests are available, the PD diagnosis usually involves lab tests to rule out other conditions, personal medical and family medical history, symptom history, observation by the neurologist and a UPDRS (Unified Parkinson's Disease Rating Scale now revised).
While Propranolol a beta-adrenergic receptor antagonist (beta blocker) is used by some people with Parkinson's disease with about 50% success as a treatment, it is the standard Essential Tremor treatment. Neither disease is curable so treatments to control the disease to one extent or another are protocol.
I checked Patients Like Me in the Parkinson's Community where 45 people indicated that they were or had taken Propranolol with some success for PD. Many people take it for several other conditions.
Both you and your father can join Patients Like Me. Registration is free and does provide an opportunity to learn more about the disease as well as treatments and therapies. It also gives you, as a caregiver or your father as a patient to track the progression of his condition as well as keep a record of his medications, nutritional supplements and other supportive therapies. His progression record and others he can create on PLM can actually be printed and taken to his doctor(s).
http://www.patientslikeme.com/conditions/4-parkinson-s-disease
It is, as Chris mentioned, not unusual for people with Parkinson's or any tremor disorder to feel uncomfortable in public. And I would say that this shunning of public appearance does often improve until family, friends and therapy helps to reassure the person of their self worth and safety. Yes, he may have a form of depression common in at least 40% of people with PD.
There are many ways to learn about tremor disorders but because the diagnosis is possibly questionable, you need to familiarize yourself with the other possibilities.
http://www.medical-library.org/journals3a/essential_tremor.htm
An excellent resource is We Move.org where you can begin with the Parkinson's disease section but view other options from the left margin.
http://www.wemove.org/par/
Because there are many symptoms of the disease, perhaps you and your dad could make a chronological list of his symptoms. For better understanding of his condition, read the article about the precursor symptoms common to many people later diagnosed with PD.
http://parkinsonsfocustoday.blogspot.com/2011/04/early-warning-signs-of-parkinsons.html
I would also encourage his primary caregiver or the future designee to have your father sign a medical HIPAA release at his doctors offices. When this is necessary, it could be too late for him to provide informed consent. This will also provide for the right to discuss issues with his doctor(s) in the event of unforeseen events or changes in his condition.
Many people with PD lead productive lives for many, many years limited only by their ability to push through and the difference in being a person who happens to have PD and a person who defines himself (herself) by the disease.
You would do well to acquaint yourself with the current therapies and treatments for PD. Although I would add some off-label treatments to the list below written in 2009, it is still timely:
http://parkinsonsfocustoday.blogspot.com/2009/12/treatments-for-parkinsons-disease.html
At some point your father might be able to go through his grieving process about the diagnosis but he is going to need the support of people who care about him. This isn't a wake for his past life, it is a way of planning for the journey. But don't nag him and don't plead. Remind him of the fun he's had in the past. You might be able to bring him around
I can't stress how important it is to be able to smile and to laugh to get those feel-good endorphins going. Laughter is even more important than sunshine for PD.
I can be reached through Y!A or through contact us at the site below.