Depending on where on geosphere this event occurs and how simultaneously they land it may be possible to apprehend them all with single craft.
Unless they land close by, it isn't. Base missions have 6 UFOs, most of which land for 2x4 hours, and the Battleship lands only once for five, so it's got to be the first or second target. Even the Avenger can fly to about a quarter of the globe (which I think is a reasonably average distance) 4-5 times in 8-10 hours, and then needs most of a day for refueling (and at least three hours for another mission if you launch it early, so the UFOs are most likely gone by then). Unless you want to waste time and fuel tailing them to get a leg up on the first mission, which is worse. And
of course the aliens will choose to build their base nowhere near where the Avenger is currently stationed

, so getting 4-5 out of 6 UFOs is not a guarantee.
The Ironfist has twice the flight time so can only do two missions, though it refuels
much faster. Maybe three if the stars align.
The Kitsune goes the same distance in about five hours and can do it twice, so you get
maybe two UFOs.
The aliens can also happen to schedule another mission at the same time, so that's another UFO or two somewhere entirely different.
So unless you use the Avenger, it's not even close.
Or just leave them alone, you cannot prevent base construction anyway, and it is not strictly required to get them all.
No, but I
want to loot them all for cash, Elerium and score (I get
paid by score

).
And this event is quite rare.
About 10% per month once your're well into the second year of the invasion. Kinda rare, yes.
And who will be in additional crafts? Rookies?
The second and third strike team and/or their backups. You spread your missions around with multiple strike bases. Rookies with training and transformations are also kinda passable.
Seriously, why Kitsune is in a game in the first place?
AFAIK, it's something Solarius either made up or adapted from somewhere obscure. Why it comes when it does, well, he's kinda attached to it.

As an aside, I'd like more multi-UFO missions. I was a big fan of the UFO 'swarms' back in UFO:ET's Unimod/Bman's mod. Xenonauts also hits you with a bunch of them in close succession.