I am about to start laying a brick paver walkway, part of which will be going on top of an existing, decorative, sealed concrete patio. Can I mortar the outer most bricks directly to the concrete and then fill in the remaining pavers or is there a better way? Will the morter hold?

There are a few things I'm not certain about from your description.

The walkway us partly over patio and partly over what? Earth? Crushed concrete and a sand bed? And I'm just having a hard time picturing what you mean when part of the paver walk is over a patio. As in there will be two levels? With a raised walk over a patio?

I have never done this but I wonder if the sealer on the decrotive concrete will compromise your bond? If I was doing it, I would do a little grinding first. I know it is messy, awful work but, it is better than a poor bond.

The pavers that are going on the concrete can be mortared. See if you can scuff (use a grinder) the sealer where the pavers will go.

Make sure not to span any pavers from the walkway onto the patio, they can crack and pop loose. Make an expansion joint where the walkway pavers will meet the patio pavers. Then if anything settles you won't have bricks from the patio sticking up higher than the walkway causing a trip hazard.