Did you find an interesting loophole? The idea being roughly: "so long as I transmit my callsign within 10 minutes of an annoying transmission, it's legal".
There's at least three restrictions I see against an example like the one you give. I don't think there's really any loophole here.
The biggest obstacle I see is in the identification requirements themselves. The rules don't simply say "transmit your callsign" but rather:
Each amateur station, except a space station or telecommand station, must transmit its assigned call sign on its transmitting channel at the end of each communication, and at least every 10 minutes during a communication, for the purpose of clearly making the source of the transmissions from the station known to those receiving the transmissions. No station may transmit unidentified communications or signals, or transmit as the station call sign, any call sign not authorized to the station.
— 47 CFR 97.119(a), emphasis added.
In short, your thought experiment fails this requirement. You have transmitted your callsign, yes, but it was not for the purpose of clearly making known the source of your (earlier, malicious) transmissions.
The other prevention against this, a little more of a grey area perhaps, is whether your initial "kerchunking" was a legal transmission to begin with.
The closest on the list of authorized uses of the amateur airwaves might be:
Brief transmissions necessary to make adjustments to the station;
— 47 CFR 97.111(b)(1), emphasis again added.
Whereas
false or deceptive messages, signals or identification
are prohibited by 47 CFR 97.113(a)(4)
It could be argued that your kerchunking was unnecessary and/or that your later identification as an "innocent check-in" to the net while not false was deceptive. Thus neither your kerchunk nor your check-in were necessarily legal to transmit in the first place.
To be clear, while it would still be impolite I think it would be legal — if truly testing access to a repeater! — to kerchunk a few times and then fess up with your callsign shortly thereafter. But your example is neither: the initial unidentified transmissions were not for an authorized purpose, nor does the later callsign transmission identify the earlier transmissions.
Underlying this is the fairly unambiguous rule that
No amateur operator shall willfully or maliciously interfere with or cause interference to any radio communication or signal.
— 47 CFR 97.101(d)
And yes, even though the repeater may not have been in use I suspect deliberate repetitive kerchunking would still count as:
Harmful interference. Interference which endangers the functioning of a radionavigation service or of other safety services or seriously degrades, obstructs or repeatedly interrupts a radiocommunication service operating in accordance with the Radio Regulations.
47 CFR 97.3(a)(23), emphasis added
Finally, while the recourse isn't 100% clear, it looks to be within the rights of a repeater operator to categorically ban usage by any/all kerchunking stations:
Limiting the use of a repeater to only certain user stations is permissible.
— 47 CFR 97.205(e)