Not exactly - the converters referenced in that download are for converting from other software, not for the UTF8 conversion. The UTF8 conversion utility is always included with the download.
The error would seem to indicating that your blog_entries.entry_content column is likely not UTF8 presently, and at least one row has enough data stored in the column that when converting it to UTF8, the data would exceed the amount that you can store. For instance, if you are using latin1 and the column is currently TEXT type, then converting from a single byte character set to a multibyte character set results in too much data being stored in the column. It's a fairly niche scenario to find yourself in.
You can likely work around this by changing the column type to allow more data (e.g. if the column is currently TEXT, change it to MEDIUMTEXT), and then continue the upgrade. Or you can submit a ticket if this occurs when attempting to upgrade your live site.