That's unlikely. You're falling into the common trap of assuming laws and computer source code work the same way -- you have a set of instructions that you evaluate from top to bottom until you get an answer. The law doesn't really work that way; there are laws, but there are also reasonable humans deeply embedded in the process. So in your case, you'd have to be the author of some AGPL software, have some third party install it on GCP, and then sue Google to get the GCP source code. Google would send a representative that says "this is a generic platform where anyone can run any computer program they want; we don't suggest that users run this AGPL program, and we have no way to detect that they're running it; this is an issue between Company X and the author." The judge and jury would then see that Google has absolutely no control over that license infringement, and would probably not award you their source code. It would just be unreasonable to any normal person for Google to be involved in your contract; they took no action to enter into a contract with you, after all. No cloud platform could ever exist if they automatically became parties to random software contracts. The legal system would take all of that into account when deciding how to make you whole.

Similar arguments would involve suing Intel for copyright infringement because their memory controller copied copyrighted information from RAM into cache. That's copying! But ultimately, Intel is just infrastructure; some user got the copyrighted data into RAM and knew full well that CPUs copy it into cache from time to time. That doesn't make Intel a party to your copyright infringement lawsuit, even though they did instruct the infringer's device to make a copy without your permission. It simply isn't reasonable -- no efficient CPUs could be manufactured if you won your lawsuit. So it's unlikely a court would hold Intel responsible.

Finally, there is the classic "if you read this, you owe me $50." You just did! But any court would find that an unenforceable contract because you didn't really consent to it. So I won't be suing you for $50. The world couldn't function if I could do things like this. So contract law exists without that particular contract being valid.

Thank you for taking the time to spell this out.

Some companies do read the AGPL that broadly. That's why Square requires its own customers to not use AGPL software. https://squareup.com/us/en/legal/general/pos

Wow, that "under any circumstance" is dangerously broad as a prohibition... Courts could very well read that phrase to override the assumption that otherwise might exist that actions unrelated to the services purchased from Square are outside of scope of the contract. It shouldn't jeopardize a company's ability to use Square if an employee plays with MongoDB on their corporate workstation. I realize enforcement wouldn't target this in practice, but the wording is sloppy enough to arguably bring it into scope.

Also very weird is that the Canadian terms are dramatically different and don't mention this restriction at all. In fact the whole long list of prohibited stuff in section 3.II.B is absent, even though both countries' terms cover the Online Store service in which the US terms include this wording.

Given that, maybe the true cause of the wording is boilerplate wording from their US lawyers which their Canadian lawyers don't have in their boilerplate? It's not simply about Square Canada being less of a liability risk than Square Inc, as most provisions of the Canadian terms do have Square Inc as the contracting party.

It would mean that because GCP is not itself under AGPL, you are not complying with the license, so you could be sued by the maker of the software for copying it to GCP. You are doing the copying, you are breaking the copyrights.