How old/congested with spyware and shitty programs is your computer? That really shouldn't make that much of a difference on modern multi-core CPUs. RAM and SSDs and all that will make way more of a difference. Unless you have every single updater running and a bunch of shit like McAffee antivirus and spyware and shit the hit shouldn't be that big.
It would more likely be firewall settings or something like that. Get CCleaner and fix issues in your registry and disable all the shit that automatically starts every time you start your computer and all that.
I don't know what DAW you use, but REAPER has a "performance" display, I configure it into the bottom. The only plugins that really tax it are shit like Native Instruments Kontakt. You can run like, 16 separate instances of amp sims on most modern computers before you will actually start to take a hit.
Disabling the internet connection isn't actually going to do much of anything. You are much better off downloading CCleaner and messing around with what automated tasks and shit launch at startup. There's a lot of shit that can affect how well your stuff runs, including how fastidious you are with optimization and computer hygene and all that, but just disabling the internet isn't the best way to treat that, that might treat some of the problems in a round about way somehow, but it's not addressing the root cause. There are a lot of intricacies sure, some plugins won't run unless you are running the daw .exe as an administrator and shit like that, but disabling the internet isn't the way to treat that.