Yes - I shoot a SMLE Mk III - I just shot a 100 pound wild boar with it this year in West Texas.
It is not extremely smooth, it's not particularly accurate, and it kicks like a mule, but I love it anyway. Without question, it is an amazing piece of history. No other rifle has served in as many armed conflicts over history than the British 303 and in so many ways it represented a move to the 'modern' military rifle, when introduced a century and a quarter ago.
My advice would be to use it within its' limits. Don't try to scope it -I have found that for shots I can confidently shoot with the open sights, the rifle can make the shot too. If I tried to make 250 yard shots with a scope - well, the rifle is just not quite that accurate.
It should serve you well - as it did the British Empire for half a century. Enjoy shooting, and owning a piece of history.