No, the tank won't be fine and without sounding horrible you really need to get your tank cycled;
Tank cycling; simple breakdown;
Fish poo+wee+uneaten food=ammonia (toxic to fish) in a cycling tank ammonia is broken down via nitrosomonas bacteria and becomes....
Nitrite (also toxic to fish) again in a cycling tank this is then broken down via nitrobacter bacteria and becomes....
Nitrate which is only dangerous to fish in high quantities....
Without the cycle having taken place the nitrite and or ammonia will be at a level that can poison your fish.
What to do?
1) You need to perform 20% water changes daily, if not more. I did bout 60% a day when i was in your situation and gradually reduced them as time went on.
2) You need a water testing kit (liquid not strip) to monitor the levels of toxins in your tank.