No, it is not possible. Per the help file:
The closest facility and OD cost matrix solvers perform very similar
analyses; the main difference, however, is in the output and the
computation speed. OD cost matrix generates results more quickly but
cannot return the true shapes of routes or their driving directions.
It is designed to quickly solve large M x N problems and, as a result,
does not internally contain the information required to generate route
shapes and driving directions. Alternatively, the closest facility
solver returns routes and directions but performs the analysis more
slowly than the OD cost matrix solver. If you need driving directions
or true shapes of routes, use the closest facility solver; otherwise,
use the OD cost matrix solver to reduce the computation time.