False, the trojan may not work as intended however you can still get it/infect your pc.
Also thats only a specific type of trojan I am talking about. Certian new breed trojans and almost all keyloggers send stuff outbound (IE they get your info and mail it ,ftp,http transfer w/e) to a dump site where others will read the information. Unless your firewall is setup to restrict outbound traffic (not likely) then the program could/well still work.
Similar new trojans use client initiated remote access (similar to that of gotomypc or bomgar) where the client (IE you dummy) click on and accept that someone can remote into your PC (obv they write the code to by pass the acceptance)


enjoy your stay on the net