Don, setting aside accounting policy, to answer your original questions:

(1) Does GnuCash recognize unrealized gains/losses of investments such as
stocks
Yes it does.

(2) so that they would appear in an Income Statement for a given period?
No, they do not appear on the Income Statement until the gains/losses are
realised.

(3) and in a Balance Sheet for a given date?
Yes, the Balance Sheet calculates and shows a one line *total* of all
unrealised gains/losses.

(4) And if so, how/where?
Unrealised gains/losses can be shown for individual investments on the
Advance Portfolio report.
I have attached copies of each of these reports for you.

(5) can one control the presentation?
All gnucash reports can be customised to some extent.
Suggested reading:
https://www.gnucash.org/docs/v4/C/gnucash-guide/ch_reports.html

Hope this helps.

Geoff
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<http://gnucash.1415818.n4.nabble.com/file/t379090/gnucash_income_statement.jpg>
 
<http://gnucash.1415818.n4.nabble.com/file/t379090/gnucash_balance_sheet.jpg> 
<http://gnucash.1415818.n4.nabble.com/file/t379090/gnucash_advanced_portfolio.jpg>
 




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