But, the Archer timeline is needed for the Borg stuff to happen, and was a part of the "Pegasus" (TNG) events (a story that exists in the "original timeline"), not to mention touching the mirror universe and Data's creation. Headcanon can be whatever you want, but the facts all point to the conclusion that the so-called Archer timeline was always a part of the "pre-Archer timeline."
Going with the "flexible" timeline of Star Trek, my view is that it's a matter of degrees rather than kind.
Hypothetical Timeline
Point of Divergence (First Contact): Zephram Cochrane was always part of Star Trek's history (Timeline A) but he became a much nicer and less bitter man as a result of his encounter with Picard as well as more devoted to "selling" spaceflight to the world--which resulted in things being slightly more advanced as well as important than they were in the (Timeline B).
Point of Divergence (Enterprise): Captain Jonathan Archer was probably always an important individual in Starfleet but it's just as likely he wasn't the Captain of the Enterprise but maybe the Captain of the Constitution with the new name a result of Zephram's encounter with Picard.
The Temporal Cold War results in a lot more technology, a war with the Xindi, and other stuff happening that makes DISCOVERY happen.
Point of Divergence (Discovery): The Klingon Empire has gone through some changes as a result of a much stronger Federation, Sulliban terrorism, and possibly a much nastier version of the Augment Virus (that happened anyway in the original timeline). So they go to war with the Federation when there was previously only skirmishes. Technology is far more advanced here but two of the biggest discoveries (irony) are classified.
Michael Burnham is adopted by Sarek when she originally wasn't because Archer helps find the Kirshara when originally the Syrannites did it alone--and maybe her parents were killed because Archer stirred up the Klingons a bit more.
What effect does this have on TOS and TNG?
Not necessarily as much as it might because the Time Police (Daniels) and other people are there to keep things going reasonably similar. The details might be different but presumably they're there to make Kirk find Khan, the Organians to prevent a SECOND Klingon-Federation War, and so on.
But details will be different like the fact the TOS Enterprise probably now looks closer to its Kelvin counterpart and so on.
Timeline-C exists now that is going to be Picard where the Federation seems a lot nastier than "All Good Things" with its planned Data-slaves, Hobus possibly being a result of these changes, and a lot more pew-pew bang-bang. Picard is still Picard and the galaxy is still the galaxy but there's a rougher more actioney overtown as well as the technology being more advanced.