It would, again, it's the same situation (well, almost the same) when Soviet shot down KAL-007, in KAL case, the Russian needed the aircraft to drift in and out of Russian airspace for it to shoot them down, because it take times to scramble those jet to intercept the aircraft. But then that KAL was flying at comair level, so it's not really that hard. You just need to scramble a fighter in time to shoot it down before it leaves Soviet Airspace.
For this balloon, this is outside the normal interception range because it was flying a bit above the maximum ceiling, on the other hand, would we actually wanted to? I mean if we are to intercept that, that probably not a job for F-15 or F-16, but rather F-22 or F-35. Which mean if we send those up and engage that balloon, that balloon would transmit anything before it goes down, that most likely would play into PLAAF hand. Which mean if we were to engage that balloon. we would most likely do it with SAM like THAAD or SM-6, those are the one that have enough range to intercept. There is static SAM equipment positioned at the coast and ship with missile just to do that.
On the other hand, as I explained, they would have and could have done it before it enter Alaska or before it enter Canadian Airspace (Which NORAD own both) but they didn't, no doubt there were a chance to engage that balloon before it enters population, but DoD did not do it, and instead put it on front page news and cry foul about China, which is quite strange, I would think if this is Iran or NK balloon, they would have just blow it out of the sky. But then if that was NK or Iran, that would have been just rudimentary balloon with no value. maybe the Pentagon think this is something worth studying on and so it just leaves it in place? Again, I don't know.