Definitely, it doesn't cancel F1 but if you use EAD from TPS, you will not considered as F1 student, so you loose your F1 status because F1 student and TPS are completely different things. TPS will protect you but the immigration status should be maintained yourself, if you fail to continue to current immigration status, TPS still protect you but seems you cannot comeback to original immigration status once TPS ends.

Just my understanding after looking many sites.