Marius,
There is no simple button to push to check the provenance of a recording. Tools like Audacity provide a fairly easy process to look at both the waveform (to check clipping and compression) and spectrum analysis (to check, among other things, hirez energy across time). Most other recording tools are more difficult and don't get you any closer.
The biggest problem is not whether Audacity is easy to use, but whether the results tell you everything you need to know. If the recording is not native (i.e has been upsampled, transferred, digitally remastered, etc) then the only things you can really discern is whether the purchased/downloaded content has been likely upsampled (i.e you paid for a 24/96 recording only to find a brick wall at 22k, no energy above it, and therefore safely discerning that the original recording was simple redbook). However, many changes/alterations/digital remastering, etc could have been done over the life of the original recording and very little or none of that will be obvious. Good luck viewing an analog recording that was transferred to 24 bit years ago, converted to an SACD (1 bit DSD), then ripped to PCM for download at 24/96. It could show any number of things.