If GGally provides a way to turn this object into a grob (equivalent to ggplot2::ggplotGrob()) then you could simply call that prior to using patchwork.

I'm reluctant to add support for strange objects beyond what ggplot2 offers, as the maintenance burden would be too high, and adding support for constructing a pairs plot is also outside of the scope of patchwork. It should be pretty easy to build on top of it, though...

This is now a solution.

wrap_elements(ggmatrix_gtable(ggpairs_plot_1)) + wrap_elements(ggmatrix_gtable(ggpairs_plot_2))