Yes. Once you select the project, click on the small blue information box that comes below (which contains the text "Project or Issue Type changed. Refresh search to update form fields."). This will show Components/Versions and there you can select the required Affects Versions.
More information at http://confluence.atlassian.com/display/JIRA/Searching+for+Issues#SearchingforIssues-SearchingparticularProjectsorIssueTypes
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