I think the answer to the question, "Can all the missions be completed with henchmen?" is probably, "It depends on what character you play." I play as a Monk and was able to complete every mission and a good majority of the bonus missions with henchmen-only parties. Thunderhead Keep took me a few tries while I was trying to pinpoint the bonus, but once I worked it out I actually had my henchmen party out of the keep and up in the northern area of the map where the Mursaat were spawning in. We just sat there and wailed on them every time they showed up until we got the message to go talk to the NPC and end the quest. But, again, I was playing as a Monk, so with Lina and Alesia's help I was able to keep up the whole group. Spells like Protective Spirit and Aegis helped a lot, in my experience. If you're stuck relying on Lina and Alesia for all your party's healing needs... then Dwayna help you keeping an all-human team alive, let alone an all-henchie team. No offense, girls.
Tetris is right about Bloodstone Fen: that is the first mission in the game where the bonus can't be done with henchmen. For the record, here is my list of bonus missions that are impossible/very tough to complete with henchmen:
Bloodstone Fen
Aurora Glade
Dunes of Despair -
Might be possible, but would be
extremely difficult
Elona Reach - Not impossible, but with henchmen you likely won't have time to complete bonus AND main mission in one go
Thirsty River -
Might be possible; make sure you have some anti-caster skills to deal with the two healers you have to take out at the end
The Dragon's Lair - Not impossible (believe it or not), just damned hard! I actually did this as a Prot. Monk/Diversion Mesmer with Fat Stephan, Little Thom, Alesia & Lina. It takes quite a while, but since the henchies are more reliable than humans I'd put more stock in your chances with henchmen than with a PuG.
Ring of Fire