I don't think so. Boromir dead, Merry and Pippin seized by Orcs, Frodo and Sam off on their own to complete the mission. How should Aragorn lead Legolas and Gimli?
'Let me think!' said Aragorn. 'And now may I make a right choice, and change the evil fate of this unhappy day!' He stood silent for a moment. 'I will follow the Orcs,' he said at last. 'I would have guided Frodo to Mordor and gone with him to the end; but if I seek him now in the wilderness, I must abandon the captives to torment and death. My heart speaks clearly at last: the fate of the Bearer is in my hands no longer. The Company has played its part. Yet we that remain cannot forsake our companions while we have strength left. Come! We will go now. Leave all that can be spared behind! We will press on by day and dark!' Our survey says: wrong. Merry and Pippin are your friends, and face torture and death, yes. Frodo and Sam, also your friends, are (probably) not in immediate danger, yes. But ... more important than anything, even the painful death of your friends, is that the ring be destroyed; and given the enormous danger and difficulty of doing this, Frodo and Sam (whatever they may have decided, themselves) need your help. Weigh it this way: you save Merry and Pippin, but the ring falls into the enemy's hands; you leave Merry and Pippin to their unpleasant fate, but you are able to help destroy the ring. The latter, though hard, is the right call.
You'll say, ah but Aragorn makes his choice and not only are Merry and Pippin saved by the ring is destroyed also. This, though, is a freakish chance. Good leadership does not base its decisions on the possibility of freakish chance. Besides, Merry and Pippin aren't saved by Aragorn and his band, but by the Ents; and Frodo and Sam did need help getting into Mordor (in Aragorn's absence they took this help from Gollum, and it nearly killed them).
In sum: bad call, Aragorn.