In a word no unless you are willing to have the whole mess fall off the wall due to the wind, the weight of the clematis vines and roses, or the mighty putty letting loose of the brick.

If you want to attach a trellis of any type, be it lattice or a wire trellis or whatever, the easiest way to do it would be to attach it with lead anchors and screws that you put into the mortar joints. This is done by purchasing a masonry bit and drilling into the mortar. You then get lead anchors that fit the size of masonry bit and bang them into the holes in the mortar. You can then use hookeye screws or regular galvanized screws to attach the lattice or trellis to the wall. In case you ever decide to remove the lattice, you can unscrew the screws, pull out the lead anchors, and use mortar mix that you can purchase at Lowes in tubes similar to what you get caulk in and patch the mortar holes.

I highly recommend wire instead of wood lattice. I have not had good results with Clematis and wood lattice. They don't cling to it and I have to manually wind them through. Wire is small enough around that they do cling.