In lab conditions, yes. In this case:
"Our attack is practical; an unoptimized version recovers the full key from a CIRCL server
in 36 hours and from a PQCrypto-SIDH server in 89 hours ... The target server and the attacker are both
connected to the same network, and we measure an average round-trip time of 688 µs between the two machines."
Note that:
• The server in this case does absolutely nothing except use the cryptographic library. Would it work on a real server that actually does something useful with the requests? We don't know, the paper doesn't try that.
• We aren't told if it works if other people are using the server simultaneously.
• They show the attack against obscure post-quantum algorithms nobody actually uses (as far as I know). Why not RSA or ECDSA or something more standard? Presumably they don't have a technique that works on those, as otherwise it'd have been a big upgrade to their paper.
• What about if you aren't running your attack physically right next to your target? Is I'm not hugely surprised Intel has limited themselves to issuing guidance. This paper continues a trend that's emerged since the first Meltdown/Spectre breaks in 2018 in which attacks become ever more convoluted, theoretical and unlikely to work outside of a lab yet they're all presented as equally important by the academics who develop them. I used to follow this area of research quite closely but eventually got sick of it. Way too many papers had some bizarre caveat buried deep in the paper, e.g. eventually I noticed that a lot of attacks on Intel SGX that claimed to leak cryptographic keys turned out to be using an extremely specific version of GnuTLS. I got curious why that might be and discovered that it was absolutely ancient, dating from many years before the papers were written. They were using it because that version had no hardening against side channel attacks of any kind whatsoever. Was that a realistic assumption to make for these attack papers? Probably not, but to notice this sort of trick you had to read well beyond the headlines.
I also remember some years ago, Google researchers got worried people weren't taking Spectre seriously enough, so they released a demo that claimed it would show a Spectre attack in action inside the browser. I was keen to see this because so many posited attacks seemed to rely on extremely specific situatons that didn't seem particularly plausible in the real world. I visited it in Chrome on macOS, i.e. one of the most predictable hardware and software environments the developers could have, and it didn't work. Checked reddit, it was filling up with people saying it didn't work for them either.
In the ~5 years since these attacks came out and started being patched in software and hardware, have there been any real world attackers found using them? Maybe but I don't remember hearing about any. State sponsored attackers seem to be sticking with more conventional techniques, which probably says a lot.