Something to be especially concerned about is the possibility of the turning flying off the lathe if the wood is not sound. If the wood is soft, or has flaws or abrupt transitions from hard to punky areas, there is a very likely chance that it will come out of the chuck. Do not use it if the tenon is not solid. That is probably the best case scenario of things that could go wrong. The worst case would be if the piece of wood breaks into two or more pieces because that is when there is a likelihood of the piece coming off the lathe at high velocity. You do not want a situation like that because it can put you in the hospital or worse. If you decide that the wood has sufficient structural integrity, you could try turning it, but stop often and carefully inspect it for problems.
In all cases, run the lathe at slow speed, listen for sound changes as you are turning, wear your safety gear, and keep well clear of the throw zone.
If you decide that it is safe to turn the piece, it will only cost you time to find out if the wood will turn satisfactorily. If you are a rank beginner, it might be best to forget about trying to turn it.
Punky wood is not easy to turn and get good results. For a beginner, it may be pushing the envelope, but if nothing else, it will show you why having razor sharp tools is important as well as proper cutting technique. If the wood is too punky, there will be lots of deep tear out.
To paraphrase an aviation saying, "There are old turners and bold turners, but there are no old bold turners."