I own both a 69er and a 29er. 69er is a hardtail, 29er is full suspension. I have timed climbs on both up the same mountains and:
- The 29er is faster, partially because of tire grip, partially because of gearing, and in my case partially because of full suspension on really rough trails. With a 11-34 casette the gearing is a little higher due to the 29 inch rear tire which means you basically have to grind up a mountain in a bigger gear.
- The 29er rear wheel definitely has a lot more grip, this is a huge difference in the terrain I ride
- The 69er feels quicker on single track. It feels quicker, it isn't actually faster. But it is a lot of fun
- On days when I am tired, I prefer the 69er on tough climbs because it has lower gearing with the same 11-34 cassette. A lot less pain but you aren't going as fast....
So, to the OP, switching to a 26er rear wheel will not make climbing any faster. It might feel less painful on some days, but you won't be any faster IMHO.