It's possible to use browser to have full VPN tunnel established. Not sure how SSL VPN policy is configured, but if it has some rules for host checker inspection, machine must pass those checks in order to have full VPN tunnel established.
Thank you for the update
Actually my question is to know if the laptop connected via VPN can be reached from the corporate network via RDP or other remote support protocol.
Do you think it is possible?
Yes, it's possible. Generally trusted machiens connected to full VPN falls inside of the network (same as LAN) so those VPN machines are reachable from corportate network (helpdesk guys) to take control.
Yes, network access link would be used in browser to have full vpn connected and don't need to have BIGIP Edge client . Browser pluggins will get installed which would allow host inspection. Please test and let us know the results