The weekday is irrelevant to CURRENT_TIME since
current_time is now. How it's presented on the front end is determined by the date formatting code on the backend, but since you are not manipulating
current_time it's of no consequence here.
Of course, all of that is academic, because if you truly want to…
…display all entries that are in the future…
…then what you really want is the built-in mechanism of
show_future_entries = 'yes'. This will accomplish the stated goal without having to create a custom search every time the template's loaded. The docs for
show_future_entries are here.
If you click through to that link, you should also scroll down to the
start_on parameter and you will see that its limitations include an inability to be dynamic: you MUST enter a fully realized date. That said, you could include some PHP to generate your relative future date, and achieve some arbitrary future entry display that way, but that's not what you asked. ;-)
Or am I missing something in your question? HTH.