Yes diabetics can eat some plums although the plums do contain a bit of natural sugar it's still safe for diabetics to consume some plums.
Plums should not raise your blood sugar too much when eaten in moderation but you still should keep a check on your blood sugar levels often especially if you're eating plums.
Plums are a very healthy snack that can help keep you healthy and provide you some energy as well.
You can eat between 18 to 20 plums per day without risk of raising your blood sugar levels and you would probably not want to eat anymore than 20 plums in a day anyway because you could get an upset stomach and probably diarrhea as a result.