No, but trunks can due to capsule corp. So by extension, any character in that universe could.
Now, Goku is foolish enough to be tricked into facing down vault enemies one on one. Even if he was warned about their ability to erase you from time, he would say something stupid like "Sounds like fun, I better be careful", then head in.
Someone like Vegeta or Frieza would just blow the entire planet up, including the vault without stepping foot inside.
Goku has a chance at dying, because he is a moron.
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Plus even if it can time travel I don't think the Vex have Ki..