Yes and no.
Yes you can add whatever fields you like to the exports.
But, no in this case, because you can only add fields from the issue being exported. Fields on other issues are not part of the current issue, so they cannot be exported as part of the current issue.
You can probably see where I am going with this - if you can come up with a way to pull the linked issue data into the current issue as though it is part of the current issue, then you will be able to export it. I do this with "scripted fields", which you can do with a few of the scripting or automation apps. (Obviously I just use the Adaptavist option as I work here)
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