Only partly, the argument that OVPN put forward had two parts:

1. They have no information to hand over as they do not keep logs.

2. There is no law that requires them to keep logs.

They proved the first part in court, but there wasn't anything in the torrentfreak article about the second point. The second point is the relevant one here as Mullvad are making both of the same claims. While they have a legal for the first one (case law) the second is still untried as far as I could tell (only made a quick search).

For the second part to be proven, somebody would need to take them to court on the second point. Nobody has tried to do that (yet) and so the question still open, and it depends on how you interpret the wording of the law https://lagen.nu/2022:482. In particular, is the definition strict enough that it applies to the operators of the hardware that makes up the network, or does it apply to a virtual service over the top.

I'm not a lawyer, there is a lot of subtlety in how §7 is written that I do not claim to be aware of, and my swedish is quite basic.