Yes, but that's what I meant with "once the life prolonging effect of the Ring is gone". He certainly wants to journey further than Rivendell when he sets out from Bag End, when he still has the Ring bolstering his physical condition. ("I want to see the mountains again, Gandalf", he says.) Hobbiton to Rivendell is no small walk for a Hobbit of 111, with the effect of the Ring fading, he has to concede to physical reality.