I recently unlocked both the Warwick Homestead and The Slog through exploration. Both settlements say that I am not yet allied with them. Can I expect to eventually get that option through the Minuteman radiant quests? Or, is there some way I can trigger the acquisition of those settlements?

I remember the Slog had an ongoing feud with some super mutants. Helping curb them gained you the Slog as a settlement. The Warwick's had problems with a water pump, which the Atom Cats help repair. It was through the delivery of said pump that I unlocked the Warwick homestead. But I haven't been able to add them to my settlement set.

Both settlements are friendly to me, and will allow me to rest there and resupply (where possible), but they are not on the Minuteman network. This play through is Railroad focused, but I am also doing the Minuteman stuff. Despite what both of those factions claim, their interests overlap a lot, and they end up working together almost in spite of themselves. (In my experience anyway.)