Hi Starlog,
Yes you can pulse secure client to connect to the SRX. You will have to configure dynamic VPN on the SRX hundred so that the laptop connects to the SRX throguh VPN and through VPN you can connect to the internal switches through SSH or telnet.
You can check the below link for details.
https://kb.juniper.net/InfoCenter/index?page=content&id=TN7&smlogin=true&actp=search
Thanks and regards,
Guru Prasad