Yes, the reputation earned on both accounts will be added.
An exception is reputation generated by interaction of the two accounts. If one earned for example some reputation points on one account from having a suggested edit on a post by the other accepted, that reputation will be nullified. And of course, hypothetically, if there are votes from one account ...
Flags used to be the right tool. The moderators could have merged the accounts and the OP would have regained control of their account.
But now they can't do that anymore.
Now you need to explain to the OP that they should register to the site, and then they can request the account to be merged. And if they don't want to do that... Well, too bad?
Is it possible? I don't think it is impossible, but I would imagine that it is quite unlikely. Merges can only be done by CMs, and before anything happens the user has to "prove" that they control both accounts. I'm not certain of the details, but according to the Help Center:
... After you contact us, the Stack Exchange Team will reach out to verify that ...
I declined the flag because there was nothing to be done. We can't merge accounts or move rep from one account to another at leisure.
Also, if I may be so bold, I thought the issue was too minor to waste time fixing. There are more important things to worry about than if an unregistered account misses out on 10 rep and unintentionally gains 6 through ...
To access your old account and/or merge it with your current (registered) one, you will have to contact the SE developers, since it will involve modifications to and searches in the database that is outside the powers of the community moderators.
Please navigate to the bottom of this page and click on the contact us link, and:
Explain that you would like ...
No. The procedure is: user registers one, the other gets merged into it.
The source is an SE employee. Although the statement is somewhat dated, it makes sense: SE should not have to expend effort maintaining cookie-based accounts that will likely get lost or split again in the future.