MyBB Community Forums

I have a subforum on my forums that are meant for use only by invitation. If someone does not have access (granted via being added to a usergroup), can they see if replies are being made in that thread via View Recent Posts or View Today's Posts?

Also, if the subforum is set up this way, do the spiderbots have access?

No they do not, and not unless you grant the Spiderbots access.