This depends on whether you want to A) launch a linux program inside WSL or B) you want to launch a windows program from a bash shell prompt.
If B) then yes if you install cygwin/bash. For example install git for windows and you have a system running under windows with bash. Then you can just run start, actually it is included as a script:
$ cat /usr/bin/start
#!/usr/bin/env bash
# Copyright (C) 2014, Alexey Pavlov
# mailto:alexpux@gmail.com
# This file is part of Minimal SYStem version 2.
# https://sourceforge.net/p/msys2/wiki/MSYS2%20installation/
# File: start
cmd //c start "${@//&/^&}"
If A) then it gets much more difficult especially if you want to launch a linux program to display a .pdf in a GUI window. Note that Windows knows to associate a default application to open a pdf file but WSL doesn't have the information. So even if you did get a Desktop running under WSL you would need to associate a linux GUI app to open the pdf.
Note to clarify, within WSL you execute linux executables not windows executables:
(WSL):~# file /bin/gzip
/bin/gzip: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.24, BuildID[sha1]=68cc3c090405cf6d40e97d2ff58085fd26940602, stripped
(WSL):~# file /mnt/c/Program\ Files/Internet\ Explorer/iexplore.exe
/mnt/c/Program Files/Internet Explorer/iexplore.exe: PE32+ executable (GUI) x86-64, for MS Windows
(WSL):~# /mnt/c/Program\ Files/Internet\ Explorer/iexplore.exe
bash: /mnt/c/Program Files/Internet Explorer/iexplore.exe: cannot execute binary file: Exec format error