If Channel name is not supported on windows filesystem mirc cannot log it. Example if channel name is just #>

Did you try this or are you just assuming this is the case? mIRC converts log names to be compatible with the windows filesystem. It uses an algorithm which is exposed by the following identifier:

//echo -a $mklogfn(#>) returns #_.log

Therefore the file should correctly log. Note that if you had #> and #< they would log to the same file though-- blame windows for this, not mIRC, as there's not much else it can do.

This is the contents of my logs\#_.log after joining #<:

This the case for any channel with \, /, :, *, ?, ", <, > or | as well.

This means that you can have any channel/query window logged.
PARTS of the name will be converted \ / : * ? " and | as they are (According to windows) invalid name characters. Why? Because windows uses these characters. How?
C:\WINDOWS\
"C:\Documents and Settings\Ahmed\My Documents\"

And also in DOS prompt. C: dir ? blah | bleh etc...

You can simply name your channel #&#3665;&#1769;&#1758;&#1769;&#3665; and you WILL find #&#3665;&#1769;&#1758;&#1769;&#3665;.log as windows will not complain about these characters.