Yes, you will be able to login JIRA using users in Crowd if it is setup properly. You won't have to create a local account in JIRA for each user, but you have to make sure the group for the users in Crowd is included in JIRA Users in the Global Permissions.
The following link might help https://confluence.atlassian.com/display/CROWD/Integrating+Crowd+with+Atlassian+JIRA
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