Possibly. What sort of dog, agility, and has he/she done anything like it before, can you rely on the dog to just do the right thing, or by command? I take it you haven't done it. Has it got a decent harness, like Ruffwear, that you can attach a length of rope to... Leads are too short and recoiling leads are too flimsy to be much use.
There are narrow paths above vertical drops, and one section that is very narrow with a lateral crack across the ridge with a cliff on one side and very steep ground on the other. A slip by either of you will end in tears. Not all the dodgy bits can be bypassed.
I dont want to say yeah, nor put you off totally. Only you know your dog well enough to decide what it is capable of. Since you seem unsure perhaps a few light scrambly bits like the nose of Catbells, 4 rock steps on Robinson and the bit up from Scarth Gap to Haystacks just for some confidence and assesment?