If I do a full MySql restore from a dump file, will the user permissions and privileges restore aswell?
Yes, if your mysqldump is backing up all databases!

If not, for future make sure you use --all-databases with mysqldump.

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but this will take your system to the state what it was earlier...
If you know what your java programs are connecting using (user-name and host) then you can choose to fix the permissions for that!!