Could this happen?

No, It’s too complicated. I’ll be way oversimplifying, but the following concepts remain valid:
3000+ counties run American elections. These 3000+ counties are divided into many precincts, as many as 4000+ in LA. Let’s assume that there are at least 100,000 precincts in the US (I think there are many more). A precinct’s ballot will include its own local races, such as for a school or park district. These can very easily be different from the races in a neighboring precinct. Plus, the order of candidates’ names may be different from precinct to precinct, not alphabetical, so Abrams would not always appear before Washington. For an adversary to print out millions of ballots for the US, each of them must be printed with the exact contests found on the official ballots for that specific precinct, in the exact order. Anything else would be spotted by the ballot scanners, which are computers. Take away: ballots are often are very different among tens of thousands of precincts.
My 2018 California ballot had 17 propositions, each with a paragraph long description, in English, Spanish and Chinese. The descriptions do not have to be exactly right, as the ballot scanner does not read them. But a sharp-eyed human may spot a difference, raising a red flag. An investigation would find the other ballots with the same error, triggering further investigation.
That’s not all. Some ballots come with bar codes printed on them. Figuring out what the algorithm is for determining the bar code(s) for each precinct would not be simple. Again, if it’s not exactly right, the ballot scanners will spot it. Take away: An adversary would also have to get any bar codes exactly right.
(A Hart-Intercivic sample ballot, with bar codes)
That’s not all. Ballots must arrive in sealed envelopes with the voter’s signature, which must fit with the voter’s address. This information is in many corporate databases, but you also have to know that they have not already voted, since too many double ballots coming in from the same voters would raise a red flag. Plus these envelopes also have those nearly indecipherable bar codes on them. Take away: an adversary would also have to get the envelopes exactly right too.
Conclusion: it’s possible that sending out millions of fake mail ballots to tens of thousands of different precincts is something that could be managed by Santa Claus, but not by any of our adversaries. For each precinct they would have to get the contests, their order, the bar codes, and everything on the envelopes exactly right. That’s way, way, way too complicated with millions of ballots.