We may not be able to draw a "definite conclusion," as you put it.
Jesus certainly spoke to Satan (or more accurately, communicated with Satan) on a number of occasions, particularly when the devil tempted Jesus to step outside his Father's will during Jesus' 40 days in the wilderness. In Luke 4:8 we read,
And Jesus answered and said unto him, "Get thee behind me, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve" (my italics).
Interestingly, Jesus also addressed Peter as Satan(!) in a similar fashion:
But Jesus turned, and said unto Peter, Get thee behind me, Satan: thou art an offence unto me: for thou savourest not the things that be of God, but those that be of men (Matthew 16:22 KJV with my italics).
Also in Mark 8:33 KJV:
But when he had turned about and looked on his disciples, he rebuked Peter, saying, Get thee behind me, Satan: for thou savourest not the things that be of God, but the things that be of men.
In fairness to Peter, notice that when Jesus turned to rebuke Peter for suggesting he could sidestep the cross which loomed before him, he "looked on his disciples" and not just Peter. Peter may have been the first and only disciple who protested Jesus' insistence on going to Jerusalem to be killed, but I'm quite certain the other disciples were on the same wavelength with Peter (see Matthew 17:23 NKJV).
Where, then, does this leave us? First, if Jesus were addressing Satan when he told Judas to do quickly what he had planned to do, Jesus could have said to Judas what he had said to Peter some days (or weeks) before; namely,
"Get thee behind me, Satan."
Jesus did not say this, however. For one thing, Jesus had not been conversing with Judas one-on-one prior to announcing one of the twelve disciples would betray him. Furthermore, had the disciples put two and two together when Jesus spoke to Judas, they would likely have prevented Judas from leaving the upper room.
I've always wondered why the disciple whom Jesus loved (viz., John, the son of Zebedee), the one who asked Jesus who the betrayer was, did not seem to make the connection between Jesus' sharing of the sop with Judas (which Jesus said he would) and Judas being the betrayer.
The text of the Last Supper, however, sheds light on this apparent discrepancy by telling us that when Jesus addressed Judas, some of the disciples (perhaps even John!)
thought that, because Judas had the moneybag, Jesus was telling him, “Buy what we need for the feast,” or that he should give something to the poor. So, after receiving the morsel of bread, he immediately went out. And it was night" (John 13:29-30).
Perhaps John and the other disciples were a bit slow on the uptake, but notice that Judas hightailed it out of there immediately, before the disciples had time to process what had just happened.
In conclusion, I think it highly unlikely that Jesus addressed Satan only. I think it more likely that Jesus addressed both Satan and Judas, even though Jesus did not address Judas as Satan, as he had addressed Peter some time before this incident occurred.
Most likely, I believe, is that Jesus was addressing Judas only. His instruction to Judas to do quickly what Satan had certainly tempted him to do (namely, betray Jesus to the elders, chief priests, and scribes for a mere 30 silver coins), let neither Judas nor Satan off the hook, however, since they both shared the blame for betraying the Son of Man, just as Jesus predicted they would,
Now while they were staying in Galilee, Jesus said to them, "The Son of Man is about to be betrayed into the hands of men, and they will kill Him, and the third day He will be raised up." And they were exceedingly sorrowful (Matthew 17:22-23).