yeah, you can, but after a while you will be forced to rest. But I guess that's a good schedule, just training hard and resting when you really have to, instead of allotting a specific day to rest.
Depends on what commitments you have that impede recovery such as work, studies etc. Recovery can also depend on the individual, some people are just more durable than others and can push their bodies harder.
We trained 6 days per week up at Galaxy. Six days on and rest sundays. Rest is hugely important, to allow your muscles to rebuild and grow. But you must break those muscles down first.