Do I need to suplimentary seal the joint between pavers and patio edge when that joint is used as a drain channel

Here is an idea that might work for you...

Here is a revised drawing added to the first one, with the idea you had given to you and I added where the various barriers need to be.

I forgot to note in the drawing that the gray line is the filter cloth.

The full wrap of the plastic membrane will keep the excess water from migrating back to the house. Just placing it against the wall and the bottom will allow it to get to the walls still. Remember it will be a LOT of water concentrated there.

The plastic liner will act as an in ground gutter to move the water, so be sure the bottom is accurately graded towards a place the water can flow that will do the house no harm.

If you're going to pull up pavers to install a french drain, you might as well just pull up all the pavers and get the slope correct instead.

A well laid patio should naturally shed water via its pitch. The ideal solution is to pull up the pavers, re-grade the base layer (should be sand directly under the pavers) and then lay it all back down...perhaps with a slightly exaggerated pitch this time.

If you insist on a drain, I wouldn't bother with a french drain and instead consider a surface drain:

It'd be a lot easier to install.