It is possible for a wand to hold a bit of a person's soul. But that wouldn't necessarily assure control over the wand.
I'd say true wand allegience cannot be won by encasing one's soul in it, based on what canon information we have about wand ownership (wands being passed on by defeating the previous master) and from the following example -
Considering how Dumbledore explains that Harry's wand contained a bit of Voldemort and recognised Voldemort as both kin and as mortal enemy, and acted on its own accord, I'd say, making the Elder wand a Horcrux might have had a similar effect.
"I believe that your wand imbibed some of the power and qualities of Voldemort's wand that night, which is to say that it contained a little of Voldemort himself. So your wand recognized him when he pursued you, recognized a man who was both kin and mortal enemy, and it regurgitated some of his own magic against him, magic much more powerful than anything Lucius's wand had ever performed. Your wand now contained the power of your enormous courage and of Voldemort's own deadly skill: What chance did that poor stick of Lucius Malfoy's stand?"
Harry Potter and the Deathly Hallows, Chapter-35, King's Cross
The bit of Voldemort's soul would definitely force the wand to obey him, but as to whether this would give Voldemort its allegiance, let us look at the above instance -
Harry's wand had a bit of Voldemort, and recognised Voldemort as kin. But its allegiance was to Harry, and hence it also recognised Voldemort as a mortal enemy, and regurgitated some of his own magic against him. The wand also imbibed Harry's (the true master's courage) So, I'd guess that in the case of Voldemort making the Elder wand a Horcrux, the following is likely to happen -
The bit of Volemort's soul in the Horcrux-wand, would definitely actively try to make the wand obey him (as we see the soul bits contained in each Horcrux trying to work in favour of the owner of the soul, and that Harry's wand also identified Voldemort as "kin" as a result of holding a bit of him) But, since Voldemort did not win the Elder wand's allegiance by defeating the previous master, and the fact that the previous master was Voldemort's archenemy, the wand would resist the bidding of the soul contained within. (Harry's wand ultimately works in favour of Harry despite holding a bit of Voldemort - since its allegiance rests with Harry, and actually uses Voldemort's own magic against him, since they are enemies)
So assuming Voldemort got hold of the Elder wand from Dumbledore, and made it a Horcrux, without actually winning its allegiance, I'd say the wand would still recognise Voldemort as both kin and mortal enemy and possess the qualities of both Dumbledore and Voldemort, and the same effect would repeat (i.e, that the Elder wand would work against Voldemort, despite the soul trying to make it do otherwise, and that it would be a struggle for the soul)