In practice, in almost all Muslim majority countries of the world, Muslim women do appear on television in various roles ranging from characters in dramas and commercials, as news anchors and even as religious scholars.
I guess the question ultimately boils down to whether or not women can be seen in public and participate in public life. There is a hardliner opinion shared by some as shown in the answer above; its derived by interpreting some sources in a certain way.
My point of view however is that Hadith and Sirah of the Prophet Muhammad (p.b.u.h) and narratives of the early Muslim community imply that there is nothing wrong with it as long as proper dress code is observed:
Women acted as medics and water-bearers during the wars fought in the Prophet's time and were encouraged to participate in religious gatherings:
"We used to treat the wounded, look after the patients and once I
asked the Prophet, 'Is there any harm for any of us to stay at home if
she doesn't have a veil?' He(Prophet Muhammad(p.b.u.h) said, 'She
should cover herself with the veil of her companion and should
participate in the good deeds and in the religious gathering of the
Muslims.'" Sahih Bukhari
Women attended sermons given by the Prophet, even had their special day. Hazrat Aisha was often consulted by the Sahabah on matters of religion and led a military campaign (Battle of Jamal). Caliph Umair ibn Khattab appointed a learnt woman named Al-Shifa bint Abdullah as a market supervisor to ensure that merchants didn't cheat the people.
If women did all this during the lifetime of the Prophet Muhammad(SAW) and his closest companions then what is wrong with appearing on television ... especially if its for a good cause.