This does seem like if allowed, it could possibly open up the door to more arena skips, which would not be in the spirit of this category. Then again, the trigger might as well have been placed too low, and you could just jump over.
Overall, I would not call this a glitch. Also looking at the current route and how it requires you to fight to get upgrades that are needed to go fast, I don't think this would trivialise the run, and the slippery slope this could be is not that deep. I don't think this would be beneficial until after Infierno, as you are basically "done" with upgrades and collecting money.
In terms of unintended mechanics, this falls between wallhopping and swaphopping, when looking at possible time saved, edging more to wallhopping and something that can be allowed in this category.
Overall, I do think that, in it's current state, it should be allowed, but something to keep an eye on.