No.
Sephiroth needs to get
near him. I think that makes sense. Perhaps I'm just being weird, but a sword needs to be near the opponent before it can cause damage. Or, Sephiroth could throw it. In which case, Bowser could merely jump in the air, over it. At the same time, he could breahte fire down on Seph.
Still, his power to make the ground uneven and break it apart is a great advantage. This makes it hard if not impossible for Seph to attack him on foot. Therefor, he'd resort to flying at Bowser. A quick breath of three fire balls that will follow Seph or a giant blast of fire, would certainly convince Sephiroth to back off.
If he resorts to magic, it will take time. Bowser can jump to where he is(or teleport if he has the power) and knock Seph's head in. Even if Seph does get off a spell, Bowser's jumping power would definately help in him avoiding it.
The magma below is a factor. I don't know if Bowser would die if falling into it, but Seph most certainly would. That's where Bowser's power to "shake up" the arena comes in handy. One false step and he's falling to his death. And if he tries to fly upward, Bowser could blast him with some more fire breath.
Bowser's arsenal is severely limitted, but effective.
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