Sure. The real question is, did the devil talk back? Or first? For starters, let's go over why I think Matthew and Luke really expect us to believe that he did. Then we'll discuss whether _I_ think he did.
Luke's description of Zechariah & Gabriel (and Mary & Gabriel) sets us up to read Jesus as audibly hearing the devil in just the same way. In contrast, Matthew's first three chapters always have God and his angels speaking through dreams (to Joseph & the Magi). However, just three verses after God speaks audibly to Jesus at his baptism, the Devil starts talking as well. Surely, therefore, Matthew also expects us to read this passage as an actual verbal exchange.
Elsewhere in both Gospels, we find Jesus speaking to demons through their human hosts, and we could easily imagine that could be how Satan interacted with Jesus as well... that he possessed someone and strolled out into the desert. That could have been what happened... but that's not what the Gospels are telling us.
Some accept Mark's bare bones account as 'the historical version' and suggest Matthew/Luke has embellished creatively on what must have been nothing more than inner temptations within Jesus' own conscience... that Jesus (and/or Mt & Lk) merely imagined precise words to match with the devil's temptations. That's a believable scenario... but that's not what these Gospels are giving us.
Since Luke presents Gabriel as speaking audibly and both writers present God as speaking audibly, we have no reason to expect their presentation of Satan speaking audibly* should suddenly be meant as anything but an actual occurrence.
Accepting that it truly *WAS* an actual occurrence, on the other hand, is simply a matter of personal faith.
So, do _I_ think the devil and Jesus had a debate? Sure I do. Why? Why shouldn't I? (How's that for a scientific analysis!?!)
Next: Did the Devil Teleport with Jesus?
*One more, um, technical point. I'm not looking to gain experience in spooky areas, here, but I have no knowledge to suggest HOW angels would make physical sound waves pass through air without having physical lips, teeth or vocal chords. Maybe they become audible the same way they become visible - which is, by some unfathomable method! Otherwise, if what *really* happened was some form of 'loud' mental telepathy, I don't know how we'd be able to consider that different from audible speaking. But we don't know that persons listening would be able to distinguish it, either. So, moot point.