Assuming your source data contained only English and Greek characters, and was mis-exported with an ISO-8859-1 to UTF-8 conversion (rather than an ISO-8859-7 to UTF-8 conversion), you can get your data back by first repeating the missed conversion the other way around, and then doing the right one.
You could use iconv for this (available on pretty much all Linux distributions, and on Windows via gnuwin32).
You'd do something like:
$ iconv -f UTF-8 -t ISO-8859-1 < bad_dump_file.sql | \
iconv -f ISO-8859-7 -t UTF-8 > good_dump_file.sql
As an example:
$ echo -n $'\xC3'$'\x90' | iconv -f UTF-8 -t ISO-8859-1 | \
iconv -f ISO-8859-7 -t UTF-8 | hexdump -C
00000000 ce a0 |Î |
00000002
And 0xCE 0xA0 is the right UTF-8 encoding for Π.
Is it safe to assume columns of NVARCHAR, NTEXT, NCHAR, BIT, INT, DECIMAL, FLOAT, and DATETIME all MUST be UNICODE...
Only the XML and N-prefixed types (NCHAR, NVARCHAR, and NTEXT [which has been deprecated since SQL Server 2005 was released so please do not use it]) are Unicode. Those other types you mentioned are not strings and are not stored as strings, hence they are not relevant to this question.
... and therefore WILL NOT have any characters unable to be converted from UTF-16LE to UTF-8...
This is not exactly a valid question. Unicode characters are Unicode characters regardless of their encoding, whether it is UTF-8, UTF-16LE, UTF-16BE, UTF-32LE, or UTF-32BE. Now, it is possible for the data itself to contain invalid sequences, such as invalid Surrogate Pairs. But then those aren't valid characters in the UTF-8 or UTF-32 encodings either.
... simply by exporting the values to a .txt file and resaving them with the UTF-8 Encoding prior to importing them to MySQL?
Well, you need to be sure to save the initial export file with a Unicode-encoding. So you would use either the -N or -w options with BCP.
Also, make sure that you are doing more than just changing the Byte Order Mark (BOM) of the file and are actually converting the Unicode / UT-16LE characters to UTF-8.
Best Answer
A possible solution:
mysqldumpor any other favorite tool