The license given to a radio station (whether analogue, digital, or online) grants the station the right to play music to the public. The license is granted by the relevant collection society (eg, PRS in the UK) and the fee is proportional to the max amount of possible listeners at any given time (for big station this is often quoted as 'reach', for online stations this is determined by the connection limit of the broadcasting server).
The license granted to you should be available to you for survey, so your question will be ultimately answered by looking at the license. To the best of my knowledge, nowhere in the world such license spells any restrictions on the music being played - that is to say, there is no further need for the station owners to check whether or not they are allowed to play a specific track. Such a requirement would render the day-to-day running of any radio station impractical.
However, as a business, the radio station must own all the music it is playing. That is, it may be required to provide a proof of purchase for all the music being played (with the exception of free promotional copies or Creative Commons music with the appropriate license).
The majority of the license fee paid by radio stations is distributed to the copyright owners of the music being played in a pro-rata fashion. Thus, a radio station is required to submit cue-sheets to the relevant collection society. Local law may spell exceptions to whether this is actually required for small radio stations/businesses.