I know that greyhounds supposedly have a larger heart than the average dog, along with several other breeds in the sighthound family, of which the greyhound is a member. These larger hearts were necessary because of their history of being selectively bred to chase hare, foxes, and deer over vast desert lands. This task required lots of oxygenated blood to be sent to their muscles in order to be able to run at those fantastic speeds.
A greyhound’s large heart should not to be confused with a medical condition known to cause heart enlargement known as dilated cardiomyopathy. Their larger hearts though may have sometimes have minor heart murmurs, but generally without causing disease.
Now, something to consider is that greyhounds are built more for sprinting rather than endurance, so it would be a good idea to have a vet check to make sure that your dog's joints are in good shape and it doesn't hurt to have the vet check the heart too to play it safe. Also, it may be worthy of discussing this breed's risks for bloat and bone cancer.
With a clean bill of health, I think with proper conditioning it could be possible to run with your companion as long as he appears comfortable with it and not giving signs of tiring, but I am not a veterinarian so please don't take my word for it.