I’d say the majority don’t - but there’s a few that do (ie, like the coyote mission packs). I played through about rep 8 before i loaded mods, then finished the game on mods before picking up my first DLC, then i went through most of that :)
If anyone does do it that way, note that the DLC will likely kick off before the time that you’re currently in, and that generally the only way to play it is to start a new career(you’ll get to keep your mechs, parts, pilots and money) and then your rep and the galaxy will be reset in the DLC you choose. This can actually have some fun side-effects - like i think in mine I time travelled back to before a bunch of parts on my mechs were available - i had some spares though, but I was managing them carefully as attrition was a real thing. Also, i’ll say some of the DLC is really tough (particularly kestral iirc), and you’ll want some pretty tricked out mechs (and some spares)…i really recommend finishing off the base game before you do the kestral missions.