Nope. It is not possible to even refine your chat box to hide 'system' chat (which those notifications are).
I considered addons but rejected the idea since half my problem is not wanting to see log on/off traffic of friends but the other half is I don't want to 'push' my own log on/off out for public consumption. I don't want to run 'offline' since there are aspects to that I don't like either. Ultimately, my solution was to take my friends list to zero which is where I maintain it. This has worked wonderfully. I explained my reasoning to those in the two small guilds I belong to and have no problem checking the guild roster if I want to see who's in game.
This, in combination to adjusting my chat box to normally hide 'zone' chat keeps my chat box nice and unobtrusive. Yet I can still get whispers, guild chat, say and yell.
i think the default base chat tab has system enabled by default and cannot be removed
you might be able to toggle that by creating another chat tab and only enabling the channels you want (i have not tested this as ive never felt a reason to make another chat tab lol)
they should probably add some kind of option to the "social" options to enable or disable those since it goes through system messages (then it would be on each users preference)
i have my main house (grand topal hideaway) listed in the housing tours, it has multiple target dummies, scribing altar, and grandmaster stations (in progress being filled out), as well as almost every antiquity furnishing on display to preview them
you might be able to toggle that by creating another chat tab and only enabling the channels you want (i have not tested this as ive never felt a reason to make another chat tab lol)
Not doable without addons. log-on and log-off messages are "system" channel messages. You can't disable system channel in base game, you need pChat addon for that.