Yes, TeXnicCenter supports this feature to 100%. But as (La)TeX requires you to respect some rules about file inclusion, TeXnicCenter follows these rules as well.

Example: Consider the followings tructure:

+ "C:\Temp\Test"
      --- UpLevel.tex
       |
       |
       + "C:\Temp\Test\MainProject"
         --- main.tex
          |
          |
          + "C:\Temp\Test\MainProject\Down"
            --- DownLevel.tex
            --- Name with Spaces.tex

Now (La)TeX and TeXnicCenter require you to use the following syntax in your main file "main.tex" for inclusion of "UpLevel.tex", "DownLevel.tex" and "Name with Spaces.tex":

input{../UpLevel}
input{Down/DownLevel}
input{"Down/Name with Spaces"}

Notice, that you can omit the file ending ".tex", because (La)TeX and TeXnicCenter are guessing it. Filenames with spaces need to be quoted for (La)TeX.

But you are not allowed to use backslashes "\" like in "\input{Down\DownLevel}" as backslashes are reserved for (La)TeX-Commands. Furthermore, (La)TeX and TeXnicCenter will not find your file "DownLevel.tex", if you try to include it with a slash before the name of the subdirectory: "\input{/Down/DownLevel}".