Can we do the same for the internet brower ? ^^
"The same", no. The checks against the versionList are different to the update check performed by the browser.
That said, from what I've heard, it would be theoretically possible to use browserhax to write to the browser's save data in order to spoof that the update check has been passed. But there are two issues to consider in that regard: you need to already be able to use browserhax to do this, so people who have hit the error on original 3DS are out of luck, and it may only last for 24 hours, before the browser would check for updates again and lock the user out, so a (purely hypothetical) update check spoofer would need to be the first port of call any time you sought to use the browser.
To my awareness, none of that has been tested though, and even assuming that it would work, it's still minimally useful (temporarily re-enabling browserhax by using browserhax; why not just use browserhax if you already can?), so whether anyone will put in the work is an open question. I hope so, personally: the New 3DS's browser YouTube is far superior to the native app, but at best it's an inessential feature. For most users, the primary use for the browser
is browserhax, and spoofing the check in this way would only really benefit the small subset of users who actually want to use the browser as a browser.