>>If you get the dataset, can you apply the extra condition in .NET side? Although you can also do it in SQL.
>>
>>And may be you can apply LINQ on the result set.
>
>This was my main concern. This full text syntax is not a regular SQL syntax. So, it would have to be processed in a second level. But, I am not sure if this could work. Because, the omitted word can be everywhere and might not be found as is in the first result.

I don't see the problem. You can put your original query into temp table.
Say,

select *  into #Result from Threads where contains(Threads.Notes,"my current phrase")

if @ExactPhrase
   select * from #Result where Notes like '%' + 'My current phrase' + '%'
else
  select * from #Result