Hi and WELCOME TO THE FORUM :wave:
Simple answer is yes, there is potential for it to do damage however I wouldn't panic just yet.
When you say it won't start, is the engine turning over? But won't fire? Or will the engine not turn over at all?
If it's not turning over at all, have you removed the auxillery drive belt and checked the battery is sufficiently charged (it may not have been charging properly when the auxillery drive belt went) and then tried to turn it over?
Alan