I would. Different problems can begin to develop as the body ages and can no longer work as effectively to correct things as young cells can and the whole system just doesn't work the same as in a young dog. Platelets can start to do funny things, a heart valve start to leak, tumors form as the cells react differently to antagonists, things can begin to calcify that involve pumping blood properly, spurs form and cause enthesopathies, livers malfunction.
When you get old, you will need more frequent medical checks to be sure none of the above things are happening to your blood or organs and so does your dog. Catching a platelet count which it is borderline high is far better than finding out it is 5X what it should be and the dog in dire straits. Your dog is your best friend - be his and get his old body checked out. An 9+ year old dog is quite elderly in human terms and should have earned his right to have good medical care. And the better he feels, the better he can keep you in line and run your life, just as it should be!
