Yes, as stated on the featured article about the 25th anniversary, free account players will be able to attend any activities located on free account areas such as Thais (Time Travel Dungeon, Scavenger Hunt).
For the Scavenger Hunt, it will be required to visit one of "memorable places all over Tibia" which includes places in premium areas. So, free account players will only be able to take part in the Scavenger Hunt when it happens on a free account area (the location changes every hour).
Regarding the Time Travel Dungeon, its entire content will be accessible to free account players except for the final boss, "Lord Retro", which will only be faced by premium players.
Unfortunatelly, free account players can only eat from the ambosia buffet once, and they cannot take part in the Funfair.