It would be extremely unlikely to even happen. The chances of success are next to zero. There is always the possibility of some weird miraculous turn of events, but really... Alexander already had so much damned luck in his life in OTL. At some point, it just becomes hard to be seen as anything but ASB. But more importantly... why would Alexander even do this? He knew little of India, but knew it was there. When he conquered Farghana, he showed no inclination to push on into Tokharia to see what was on the other side of it. As far as he was concerned, it was the domain of Scythian-like peoples, which had little to offer him.
Truly, the only way I can see Alexander doing this is if he somehow loses his empire to some sort of usurpation. Even then, it seems unlikely. Alexander would take his army and face the usurper. He'd probably win his empire back in the process, because... well, can you think of any potential usurper who could plausibly succeed in capturing the western parts of the empire while alexander was off in the east, and then actually beating Alexander in the field? 'Cause no names stand out in my mind... However, provided that Alexander somehow loses his empire, though, he might then decide to go into exile with his army, seeking out "a new world to conquer". That might provide the impetus. An army trekking to the far east, into unknown lands, with no logistical base to back them up, though...? I don't see it ending well. Best case scenario, they end up esteemed allies to one of the Warring States. Glorified mercenaries, useful because they use techniques relatively uncommon in the east.
As for a Diadoch doing this... No. I just don't see it happening. None of them showed any inclination like this in OTL. Marching beyond the known horizons of the world was Alexander's passion, not theirs. Only Hephaistion shared that vision, it seems, and perhaps he only did so because it was Alexander's vision and he would simply always go wherever Alexander went. So even in the scenario is "Hephaistion lives on and becomes a Diadoch", I don't find an expedition to China realistic.
However, if I might be allowed to somewhat modify the specifics of the OP, I can think of one scenario where an expedition like this (regardless of success) at least becomes a plausible idea. That scenario, of course, is the one where Alexander lives longer. Say he succeeds in Arabia and the west, settles affairs, and... well, it depends. I don't see Alexander himself going for China. For the same reasons outlined above. If his eastern ambitions resurface, they'll take the form of another (likely ill-fated) go at India. But a considerably longer-lived Alexander can leaving his empire to an adult heir. And such a formidable empire, I think, is really the only plausible base from which to launch an expedition to the furthest east.
Say Alexander's son learns (through trade with the east) of China, and decides he wants to know more. He tentatively sends some envoys, and comes to know about the warring states. Perhaps he decides he wants a piece of that and sends (or leads) an invasion force? I think it would end poorly. The thing is, the state on the other side of Tokharia is... Qin. And Qin is really tough. An exiled Alexander becoming a mercenary in their employ is one thing, but any force from the west defeating Qin is unrealistic in the extreme. But at least the invasion happening is something that might be considered realistic. It would be stupid, but rulers of vast empires are not guaranteed to always be very smart about their choices.
Let us attempt to find a yet more hopeful variation on this scenario. Let us give Alexander's son more credit: he sees the risks. His envoys reach China via Tokharia, but also via India and Indochina. Or perhaps even a naval expedition is undertaken? (That would demand serious shipbuilding developments, but perhaps the wealth of the vast empire, combined with the ruler ordering studies into better ship design, could provide such things.) In any case: the point is that the argead empire somehow opens communications with the state of Chu, and manages to establish an anti-Qin alliance.
This would take a lot of time to set up. But let's say it happens during the next generation, and in 247 BC (when king Zhuangxiang of Qin dies and leaves a thirteen-year-old heir) Chu and the Argead empire feel that their hour has come. They execute a coordinated assault from both east (Chu) and west (and Argead army via Tokharia). Ideally, the other warring states (who by this point obviously knew what a threat Qin posed) could be persuaded to help, too. Or at least to stay neutral and not attack Chu in an opportunistic strike. Furthermore, the Argead empire might be able to persuade some of the nomadic peoples to Qin's north and northwest to join in the war (perhaps by outright paying them to do so). Following the war, the goal would be the utter destruction of Qin, the annexation of most of it to Chu, and the annexation of Tokharia and the westernmost regions of Qin to the Argead empire. Whereafter these two, presumably (or... hopefully), become trade partners and staunch allies.
That scenario is of course completely hypothetical, and relies entirely on 100% made-up personalities for Alexanders hypothetical descendants... but it is the only way I can see this happening succesfully, so that it ends with part of China (specifically: part of Qin) owned by the Argead empire. Albeit in a way that only has it happen 76 years after Alexander's OTL demise, and neither by his doing nor by that of one of OTL's diadochi.