Do they actually make that offer if you play as a Drow male?
Nope, its only mentioned by Drow male NPCs.
I believe i have heared it as reason why he joined the cult from the dead Drow on Halsin table, when i was playing Drow female and used my Racial choices.
And ARE their members in important places? Again, what information do we get that suggests this cult has meaningful reach outside of this area?
Depends ...
Minthara, Ragzlin, Gut and Nere ... all are leaders, if that is what you mean, so its obvious that you will not start as some lowly apprentice.
If you are talking about infiltrating the curent goverment ... we obviously dont know yet, since even datamining content still can be changed.

The only clue we have is the Grand Duke ... and that Deep Gnome, he isnt exactly "important person" himself, but the formula to that rumepowder certainly is important enough.

They control a temple that seemed to have already been abandoned and let them just move in, they don't really control a village, they destroyed it, just like they destroyed an inn and a tollhouse, which seems to just have been a place where this one guy and maybe his family lived, from the impression I got. And I don't think we get a sense of how much of the Underdark they control until we actually get there, I at least didn't find any hints as to what they control.
You seem to be forgetting those dead Flaming Fist soldiers all over the Waukeen's Rest ...
There certainly was some force to overcome. How big? I dunno. But to say that they just killed family of civilians would be huge understatement.

About Underdark ...
Yes, you are totally right you will know scale of their control down there only after you visit it ... but there is nothing stoping you to visit it before you even enter Goblin camp.

Larian even counts with that option by implementing conversation with Minthara after Nere send you to her, in case you get to Grimforge first and explore surface after.

As for the druid grove, that ties into a problem less with the path than with the game at large-no sense of scaling. We don't know how powerful druids are and how easy or difficult it should be for them to be threatened.
Well, we certainly know that once they find the Grove, they will massacre them all.
(even without your help, if you decide to Long Rest)
That gives me quite good image of their power.

I mean there is no reason to compare anything to PC, since PC is "allways suppose to win". :-/
But when they fight each other without us, it should tell us something.
As you've pointed out, Halsin their leader got captured by them
Did i?
Personaly i believe that Halsin was "kept in the cage" just bcs he wanted to.

Especialy since when you dont free him, but tell Minthara where the Grove is ... he will massacre them all and free himself.

So, they obviously dont even match his power.

so why should we think their ability to threaten the grove is especially noteworthy, even on top of the fact their other resistance is in the form of tired refugees.
Well, im not saying that they are the most powerfull military force in Faerun ... but the fact is that they control this region fully.
we can't actually talk about our intentions regarding the cult with our companions. We can't ever say that we're joining them with the intent to betray them to any of our companions, we don't even get the option.
Except Wyll ... if you have him in your party, you can tell him that you are just luring Minthara out so you can set trap on her ...
But yes, i agree there should be some "what are you even doing now?" conversation ... certainly +1!