If the ion pod was being "launched" then why not use the word "launch"
Because the pod would be an unpropelled rather than a propelled device, simply dumped overboard to begin its mission. You just "let it loose" and allow the storm to carry it away.
So you're saying it's disposable? As in disposable as an assumed role for it's mission? That would mean that Enterprise
is only capable of studying one, or at most two (assuming another pod in the symmetrical location on the other side of the ship), ion storms ever without a base layover. We know they can't load another one from the inside because in TOSr we see the device in question being installed from the outside of the ship.
To me this brings up some odd assumptions. Why would Starfleet require it's ships to be carrying bulky disposable single use items to cover the measurement of one fairly isolated phenomenon? If ion storms are common enough for their regular measurement and study to be a standard mission of Starfleet ships, then why equip ship's with the goods to only ever study two? If they are more rare, then why equip ships with big bulky elements that only have one, occasionally called upon use?
It seems most likely to me that the ion pod(s) are there to study ion storms and other ion-related phenomena but they aren't disposable. I posit that the ship has its shields up during the fly-through (and Yellow alert is standard practice) but for the pod to work, it must be extended on some kind of boom to outside the shield envelope, where, if things get bad, it can function in an analogous way to a sea anchor and can put the ship in extreme danger. If something goes wrong enough, then the ship goes to Red alert and the offending pod is jettisoned -- that is, cut off from the ship and ejected away in order to prevent whatever greater damage would be caused by allowing it to drag. This is an emergency procedure. If things go by the book, then after the readings are taken on the ion plates, then the whole shebang is reeled back in and the hapless crew member hops out none-the-worse-for-wear.
Why can't this whole operation be automated, sparing the risk and exposure of a crewman? Perhaps the nature of the ion storm causes interference to make computers unreliable or even non-functional. The process can only be carried out manually. This might explain how Finney got out in time without there being any record of it: since automation is unreliable, there is an emergency line which is on a spring loaded pulley system which can yank the crewman back if he tugs the cord. This is a totally mechanical system and when Finney got back aboard, he released the lock and let the line roll back into space, making it appear that he was lost and then stashed his space suit and proceeded to monkey around with the log records.
Now, for my money, this is the only scenario that makes a lick of sense. Your mileage may vary, of course. But that's my story and I'm sticking to it.