Certainly you can yes.
Depending on how active the accounts have been depends on how much or how little work is involved.
First step is work out if either can just be deleted - it could be that if one of the accounts has not reported (reporter) or worked on (assignee) or made any comments, then just try administering the account and deleting it.
Assuming that does not work, when you try and delete an account, it gives you useful information needed for your next steps. There may be issues reported - click on the link provided and it will take you to a view of those issues, what you do next is bulk edit all of them and change the reporter to the other account. You then do the same for assignee.
Only thing that may remain is 'commented on tickets' - if that's the case there is a plugin out there in the Marketplace that allows you to change the 'Commenter' to the other account.
https://marketplace.atlassian.com/apps/1214301/comment-toolbox-for-jira?hosting=server&tab=overview
Works well and I've done it quite a number of times.
HTH
Gav...
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