Is my newly fitted boiler safe?

It is probably safe, you might just end up with a wet floor if there are no pipes going to drainage, however if you are living in rented accomodation i believe you could get your landlord severely punished if they have used a tradesman who is not gassafe registered as by law anything gas powered in rented accomodation has to be checked and certified and passed off by a gassafe registered engineer, even gas fires, cookers, hobs, boiler etc. even if they have beeen there years, the landlord can carry out the work thereselves but it will have to be certified before you can use it