Sure it does. I've been a Trek fan for 35 years and I have no problem whatsoever in connecting SNW with the rest of Trek. Does it occasionally require a little creative thinking on my part? Sure! But that's always been the case. It's half the fun of being a Trekkie.
Yes... but... the new stuff is increasingly difficult to connect. I do enjoy conjecture about some apparent continuity errors, but hot damn have they piled up.
I can accept ENT being before TOS, and TNG being after TOS.
It's much more difficult to create a world where DSC and SNW take place so close to TOS... they are inherently incompatible.