Yes. The more experienced you are, the more your network does all of your job searching for you in the background. (Of course, this assumes you are actively building and maintaining your network.)
I'm not sure it's just a network thing. Certainly you need experience to be a great engineer, but I've known plenty of engineers with 30 years experience who find themselves competing with everyone else when they lose their job.
The best engineer I've ever known spent most of his career doing drivers at Qualcomm. When he left his job they offered him significant raises to stay, offered months of paid leave, and then said he could always come back. Later, an OSS project he worked with heard he was free, and they changed their remote work policies to hire him. He's under 30, and despite working remotely at an OSS project makes significantly more than me.
I like to think I'm a good engineer, but when I work with customers they aren't setting linkedin alerts on my name for if I leave my job. To qualify for what this article is getting at, you really need to be the best engineer out of 100's, not the best engineer in your team of 5.
> this assumes you are actively building and maintaining your network.
Frankly, being a consistent super-star engineer on a team of good engineers, is more important than actively maintaining a network. Experienced founders ask everyone in their small circle of long-time, highly credible, proven associates "who's the best engineer you've ever worked with?" If the answer is interesting, they follow up with "Where are they now?
In my startups, I recruited nearly all of the star engineers this way. In most cases, getting them on board required significant sustained effort. Sometimes just finding them wasn't easy. So - if you're really the engineer on your team who most everyone else would identify as "the best", please don't waste any time maintaining a network. Just keep doing truly great work that others will still be telling stories about over drinks years from now.
If you're not that engineer... then by all means be a reliable, likable, good communicator and maintain your network! Because as a founder, I never had enough high-credibility sightings of "great engineers" in the wild, so I had to mostly build teams out of credible referrals of best "good engineers" and even best "intern or new grad engineers with potential" you've worked with.