nothing is impossible if you planned it right and have luck but personally i like more to travel than to go sightseeing
since it would be your first interrail trip i suggest you to go to fewer cities and have some days to relax or see them better...
at the trips to come you can go to the rest...
also avoid expensive cities and countries for your first trip cause its not so easy to manage with money
my suggestion something like this..
after all its your trip so you can go to the whole europe in 30 days
just have fun and after share your experiences !